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  • 1.
    Zhang, Silun
    et al.
    MIT, LIDS, 77 Massachusetts Ave, Cambridge, MA 02139 USA..
    He, Fenghua
    Harbin Inst Technol, Control & Simulat Ctr, Harbin 150001, Heilongjiang, Peoples R China..
    Hong, Yiguang
    Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China..
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    An intrinsic approach to formation control of regular polyhedra for reduced attitudes2020Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 111, artikkel-id 108619Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper addresses formation control of reduced attitudes in which a continuous control protocol is proposed for achieving and stabilizing all regular polyhedra (also known as Platonic solids) under a unified framework. The protocol contains only relative reduced attitude measurements and does not depend on any particular parametrization as is usually used in the literature. A key feature of the control proposed is that it is intrinsic in the sense that it does not need to incorporate any information of the desired formation. Instead, the achieved formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Using a novel coordinates transformation, asymptotic stability of the desired formations is proven by studying stability of a constrained nonlinear system. In addition, a methodology to investigate stability of such constrained systems is also presented.

  • 2.
    Enqvist, Per
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Svensson, Göran
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A Marginal Allocation Approach to Resource Management for a System of Multiclass Multiserver Queues Using Abandonment and CVaR QoS Measures2019Inngår i: 7th International Conference on Operations Research and Enterprise Systems, ICORES 2018, Springer Verlag , 2019, s. 119-133Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A class of resource allocation problems is considered where some quality of service measure is set against the agent related costs. Three multiobjective minimization problems are posed, one for a system of Erlang-C queues and two for systems of Erlang-A queues. In the case of the Erlang-C systems we introduce a quality of service measure based on the Conditional Value-at-Risk with waiting time as the loss function. This is a risk coherent measure and is well established in the field of finance. An algebraic proof ensures that this quality of service measure is integer convex in the number of servers. In the case of the Erlang-A systems we introduce two different quality of service measures. The first is a weighted sum of fractions of abandoning customers and the second is Conditional Value-at-Risk, with the waiting time in queue for a customer conditioned on eventually receiving service. Finally, numerical experiments on the two system types with the given quality of service measures, are presented and the optimal solutions are compared.

  • 3.
    Enqvist, Per
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Svensson, Göran
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A state dependent chat system model2019Inngår i: ICORES 2019 - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems, SciTePress , 2019, s. 121-132Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The main purpose of this paper is to introduce a model of a chat based communication system, as well as developing the necessary tools to enable resource optimization with regards to a measure of the service quality. The system is modeled by a Markov process in continuous time and with a countable state space. The construction of the intensity matrix corresponding to this system is outlined and proofs of a stationary state distribution and an efficient way of calculating it are introduced. A numerical example for system optimization when the service measure is the average sojourn time is included as well as a heuristic algorithm for quicker solution generation. 

  • 4.
    Wang, Ximei
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Credit rating analysis based on the network of trading information2019Inngår i: The journal of network theory in finance, ISSN 2055-7795, Vol. 5, nr 1, s. 47-65Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we investigate a credit rating problem based on the network of trading information (NoTI). First, several popular tools, such as assortativity analysis, community detection and centrality measurement, are introduced for analyzing the topology structures and properties of the NoTI. Then, the correlation between the characteristics of the network and the credit ratings is investigated to illustrate the feasibility of credit risk analysis based on the NoTI. Sovereign rating based on the world trade network is analyzed as a case study. The correlation between the centrality metrics and the sovereign ratings conducted by Standard & Poor's clearly shows that highly ranked economies with vigorous economic trading links usually have higher credit ratings. Finally, a simulation is conducted to illustrate the degree of improvement in credit rating prediction accuracy if the NoTI is considered as an additional attribute.

  • 5. Hu, C.
    et al.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hong, Y.
    Distributed adaptive Kalman filter based on variational Bayesian technique2019Inngår i: Control Theory and Technology, ISSN 2095-6983, Vol. 17, nr 1, s. 37-47Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The convergence of the proposed algorithm is proved in two main steps: noise statistics is estimated, where each agent only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.

  • 6.
    Li, Yibei
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Dynamic Optimization for Agent-Based Systems and Inverse Optimal Control2019Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This dissertation is concerned with three problems within the field of optimization for agent--based systems. Firstly, the inverse optimal control problem is investigated for the single-agent system. Given a dynamic process, the goal is to recover the quadratic cost function from the observation of optimal control sequences. Such estimation could then help us develop a better understanding of the physical system and reproduce a similar optimal controller in other applications. Next, problems of optimization over networked systems are considered. A novel differential game approach is proposed for the optimal intrinsic formation control of multi-agent systems. As for the credit scoring problem, an optimal filtering framework is utilized to recursively improve the scoring accuracy based on dynamic network information.

    In paper A, the problem of finite horizon inverse optimal control problem is investigated, where the linear quadratic (LQ) cost function is required to be estimated from the optimal feedback controller. Although the infinite-horizon inverse LQ problem is well-studied with numerous results, the finite-horizon case is still an open problem. To the best of our knowledge, we propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual, where the optimality condition is solved under a static quadratic programming framework to facilitate the computation.

    In paper B, the optimal formation control problem of a multi-agent system is studied. The foraging behavior of N agents is modeled as a finite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The collaborative swarming behaviour derived from non-cooperative individual actions also sheds new light on understanding such phenomenon in the nature. The proposed framework has a tutorial meaning since a systematic approach for formation control is proposed, where the desired formation can be obtained by only intrinsically adjusting individual costs and network topology. In contrast to most of the existing methodologies based on regulating formation errors to the pre-defined pattern, the proposed method does not need to involve any information of the desired pattern beforehand. We refer to this type of formation control as intrinsic formation control. Patterns of regular polygons, antipodal formations and Platonic solids can be achieved as Nash equilibria of the game while inter-agent collisions are naturally avoided.

    Paper C considers the credit scoring problem by incorporating dynamic network information, where the advantages of such incorporation are investigated in two scenarios. Firstly, when the scoring publishment is merely individual--dependent, an optimal Bayesian filter is designed for risk prediction, where network observations are utilized to provide a reference for the bank on future financial decisions. Furthermore, a recursive Bayes estimator is proposed to improve the accuracy of score publishment by incorporating the dynamic network topology as well. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than all the efficient estimators, and the mean square errors are strictly smaller than the Cramér-Rao lower bound for clients within a certain range of scores.

  • 7.
    Zhang, Silun
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Intrinsic Formation and Macroscopic Intervention in Multi-agent Systems2019Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In this dissertation, we study two problems within the field of the multi-agent systems theory. One is the formation control for multiple reducedattitudes, which are extensively utilized in many pointing applications and under-actuated scenarios for attitude maneuvers. In contrast to most existing methodologies on the formation control, the proposed method does notneed to contain any formation errors in the protocol. Instead, the constructedformation is attributed to geometric properties of the configuration space andthe designed connection topology. We refer to this type of formation controlas intrinsic formation control. Besides, the control protocols proposed in thiswork are designed directly in space S^2 , avoiding to use any attitude parameterizations. Moreover, along the studies, some elementary tools for reducedattitudes control are developed.

    Another problem is a moment-based methodology to modeling and ana-lyzing collective behavior of a group of agents. The theory is applicable fora wide range of applications, such as multi-agent systems with interactionsas well as with leaders and/or control input, and the use of this frameworkcan considerably reduce the computational burden for controlling and ana-lyzing such systems. We therefore propose to develop and use this theory forthe multi-agent applications such as crowd dynamics, opinion dynamics andother macroscopic problems.

    Particularly, in paper A a continuous control law is provided for a reduced attitude system, by which a regular tetrahedron formation can achieveasymptotic stability under a quite large family of gain functions in the con-trol. Then, with a further restriction on the control gain, almost global stability of the tetrahedron formation is also obtained. In this work, we introducea novel coordinates transformation that represents the relative reduced atti-tudes between the agents. The proposed method is an intrinsic formationcontrol that does not need to involve any information of the desired formation beforehand. Another virtue of the method proposed is that only relativeattitude measurement is required.

    Paper B further concerns the formation control of all regular polyhedralconfigurations (also called Platonic solids) for reduced attitudes. Accord-ing to the symmetries possessed by regular polyhedra, a unified frameworkis proposed for their formations. Via using the coordinates transformationpreviously proposed, it is shown that stability of the desired formations canbe provided by stabilizing a constrained nonlinear system. Then, a method-ology to investigate the stability of this type of constrained systems is alsopresented.

    In paper C, we introduce an approach for modeling collective behaviorof a group of agents using moments. We represent the swarming via their dis-tribution and derive a method to estimate the dynamics of the moments. We use this to predict the evolution of the distribution of agents by first computing the moment trajectories and then use this to reconstruct the distributionof the agents. In the latter an inverse problem is solved in order to reconstructa nominal distribution and to recover the macro-scale properties of the groupof agents. The proposed method is applicable for several types of multi-agent systems, including leader-follower systems.

    Paper D considers the problem of tracking and encircling a moving target by agents in the 3-dimensional space. In this work, we show that similardesign techniques proposed for reduced attitudes formations can also be applied to the formation control for point mass systems. Therein, a group ofagents are driven to some desired formation on a spherical surface and simultaneously the center of this spherical formation is kept coinciding withthe target to be tracked. By properly designing communication topology, theagents constitute a cyclic formation along the equator of an encircling sphere.

    In Paper E, a methodology based on differential geometry techniquesis proposed to investigate exponential stability of a formation for reducedattitudes. By such a method, there is no need in finding any relative coordinates, which is typically needed but shown to be difficult when the formationproblem is evolving in a non-Euclidean space. In the paper, the desired formation is treated as an embedding submanifold in (S^2)^N and by using therotation symmetries owned by the attitude dynamics its stability is directlyexamined. Moreover, such a method turns out to be coordinates free, namely,exponential stability of a formation can be completely determined by just investigating any one equilibrium which can result in the formation under anylocal chart of (S^2 )^N . This greatly simplifies the stability analysis for theformation problems.

  • 8.
    Zhang, Han
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Umenberger, Jack
    Department of Information Technology, Uppsala University, Uppsala, Sweden.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Inverse optimal control for discrete-time finite-horizon Linear Quadratic Regulators2019Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 110, artikkel-id 108593Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we consider the inverse optimal control problem for discrete-time Linear Quadratic Regulators (LQR), over finite-time horizons. Given observations of the optimal trajectories, or optimal control inputs, to a linear time-invariant system, the goal is to infer the parameters that define the quadratic cost function. The well-posedness of the inverse optimal control problem is first justified. In the noiseless case, when these observations are exact, we analyze the identifiability of the problem and provide sufficient conditions for uniqueness of the solution. In the noisy case, when the observations are corrupted by additive zero-mean noise, we formulate the problem as an optimization problem and prove that the solution to this problem is statistically consistent. The performance of the proposed method is illustrated through numerical examples.

  • 9.
    Persson, Linnea
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Wahlberg, Bo
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Model predictive control for autonomous ship landing in a search and rescue scenario2019Inngår i: Model predictive control for autonomous ship landing in a search and rescue scenario, San Diego, 2019, s. 1169-Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper presents a Model Predictive Control approach for autonomous landing of a quadcopter on the deck of a moving boat. The research is motivated by a large-scale demonstrator arena equipped with autonomous boats and drones that should collaborate to perform various tasks related to search and rescue missions. The landing maneuver is executed in a cooperative manner where both the boat and the drone take actions to reach their common objective. The maneuver is designed to be feasible under a range of conditions, including scenarios where the boat is moving across the water or when it is subjected to disturbances such as waves and winds. During the landing, the vehicles must also consider various safety constraints for landing safely and efficiently. The algorithms are implemented both in hardware-in-the-loop simulations, where we demonstrate some of the different scenarios that the algorithm is expected to handle, as well as on a real boat-drone system, on which initial tests have been carried out.

  • 10.
    Frimodig, Sara
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Schulte, Christian
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Datavetenskap, Programvaruteknik och datorsystem, SCS.
    Models for Radiation Therapy Patient Scheduling2019Inngår i: 25th International Conference on Principles and Practice of Constraint Programming, CP 2019, Springer, 2019, Vol. 11802, s. 421-437Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In Europe, around half of all patients diagnosed with cancer are treated with radiation therapy. To reduce waiting times, optimizing the use of linear accelerators for treatment is crucial. This paper introduces an Integer Programming (IP) and two Constraint Programming (CP) models for the non-block radiotherapy patient scheduling problem. Patients are scheduled considering priority, pattern, duration, and start day of their treatment. The models include expected future patient arrivals. Treatment time of the day is included in the models as time windows which enable more realistic objectives and constraints. The models are thoroughly evaluated for multiple different scenarios, altering: planning day, machine availability, arrival rates, patient backlog, and the number of time windows in a day. The results demonstrate that the CP models find feasible solutions earlier, while the IP model reaches optimality considerably faster.

  • 11.
    Sremac, Stefan
    et al.
    Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
    Wang, Fei
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Wolkowicz, Henrik
    Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
    Pettersson, Lucas
    KTH, Skolan för teknikvetenskap (SCI), Fysik.
    Noisy Euclidean Distance Matrix Completion with a Single Missing Node2019Inngår i: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present several solution techniques for the noisy single source localization problem, i.e. the Euclidean distance matrix completion problem with a single missing node to locate under noisy data. For the case that the sensor locations are fixed, we show that this problem is implicitly convex, and we provide a purification algorithm along with the SDP relaxation to solve it efficiently and accurately. For the case that the sensor locations are relaxed, we study a model based on facial reduction. We present several approaches to solve this problem efficiently, and we compare their performance with existing techniques in the literature. Our tools are semidefinite programming, Euclidean distance matrices, facial reduction, and the generalized trust region subproblem. We include extensive numerical tests.

  • 12.
    Elvander, Filip
    et al.
    Lund Univ, Div Math Stat, Lund, Sweden..
    Haasler, Isabel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jakobsson, Andreas
    Lund Univ, Div Math Stat, Lund, Sweden..
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    NON-COHERENT SENSOR FUSION VIA ENTROPY REGULARIZED OPTIMAL MASS TRANSPORT2019Inngår i: 2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2019, s. 4415-4419Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This work presents a method for information fusion in source localization applications. The method utilizes the concept of optimal mass transport in order to construct estimates of the spatial spectrum using a convex barycenter formulation. We introduce an entropy regularization term to the convex objective, which allows for low-complexity iterations of the solution algorithm and thus makes the proposed method applicable also to higher-dimensional problems. We illustrate the proposed method's inherent robustness to misalignment and miscalibration of the sensor arrays using numerical examples of localization in two dimensions.

  • 13.
    Hagrot, Erika
    et al.
    KTH, Skolan för kemi, bioteknologi och hälsa (CBH), Industriell bioteknologi. AdBIOPRO, VINNOVA Competence Centre for Advanced Bioproduction by Continuous Processing, Sweden.
    Oddsdóttir, Hildur Æsa
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Mäkinen, Meeri
    KTH, Skolan för kemi, bioteknologi och hälsa (CBH), Industriell bioteknologi. AdBIOPRO, VINNOVA Competence Centre for Advanced Bioproduction by Continuous Processing, Sweden.
    Forsgren, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Chotteau, Véronique
    KTH, Skolan för kemi, bioteknologi och hälsa (CBH), Industriell bioteknologi. AdBIOPRO, VINNOVA Competence Centre for Advanced Bioproduction by Continuous Processing, Sweden; WCPR, Wallenberg Centre for Protein Research, Sweden.
    Novel column generation-based optimization approach for poly-pathway kinetic model applied to CHO cell culture2019Inngår i: Metabolic Engineering Communications, ISSN 2214-0301, Vol. 8, artikkel-id e00083Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Mathematical modelling can provide precious tools for bioprocess simulation, prediction, control and optimization of mammalian cell-based cultures. In this paper we present a novel method to generate kinetic models of such cultures, rendering complex metabolic networks in a poly-pathway kinetic model. The model is based on subsets of elementary flux modes (EFMs) to generate macro-reactions. Thanks to our column generation-based optimization algorithm, the experimental data are used to identify the EFMs, which are relevant to the data. Here the systematic enumeration of all the EFMs is eliminated and a network including a large number of reactions can be considered. In particular, the poly-pathway model can simulate multiple metabolic behaviors in response to changes in the culture conditions. We apply the method to a network of 126 metabolic reactions describing cultures of antibody-producing Chinese hamster ovary cells, and generate a poly-pathway model that simulates multiple experimental conditions obtained in response to variations in amino acid availability. A good fit between simulated and experimental data is obtained, rendering the variations in the growth, product, and metabolite uptake/secretion rates. The intracellular reaction fluxes simulated by the model are explored, linking variations in metabolic behavior to adaptations of the intracellular metabolism.

  • 14.
    Forsgren, Anders
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Wang, Fei
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    On the existence of a short pivoting sequence for a linear program2019Manuskript (preprint) (Annet vitenskapelig)
  • 15.
    Böck, Michelle
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Eriksson, Kjell
    Forsgren, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    On the interplay between robustness and dynamic planning for adaptive radiation therapy2019Inngår i: BIOMEDICAL PHYSICS & ENGINEERING EXPRESS, Vol. 5, nr 4Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during the course of treatment, the authors propose a dynamic framework for robust adaptive radiation therapy in which a variety of robust adaptive treatment strategies are introduced and evaluated. This variety is a result of optimization variables with various degrees of freedom within robust optimization models that vary in their grade of conservativeness. The different degrees of freedom in the optimization variables are expressed through either time-and-uncertainty-scenario-independence, time-dependence or time-and-uncertainty-scenario-dependence, while the robust models are either based on expected value-, worst-case- or conditional value-at-risk-optimization. The goal of this study is to understand which mathematical properties of the proposed robust adaptive strategies are relevant such that the accumulated dose can be steered as close as possible to the prescribed dose as the treatment progresses. We apply a result from convex analysis to show that the robust non-adaptive approach under conditions of convexity and permutation-invariance is at least as good as the time-dependent robust adaptive approach, which implies that the time-dependent problem can be solved by dynamically solving the corresponding time-independent problem. According to the computational study, non-adaptive robust strategies may provide sufficient target coverage comparable to robust adaptive strategies if the occurring uncertainties follow the same distribution as those included in the robust model. Moreover, the results indicate that time-and-uncertainty-scenario-dependent optimization variables are most compatible with worst-case-optimization, while time-and-uncertainty-scenario-independent find their best match with expected value optimization. In conclusion, the authors introduced a novel framework for robust adaptive radiation therapy and identified mathematical requirements to further develop robust adaptive strategies in order to improve treatment outcome in the presence of interfractional uncertainties.

  • 16.
    Zhang, Han
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Optimizing Networked Systems and Inverse Optimal Control2019Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis is concerned with the problems of optimizing networked systems, including designing a distributed energy optimal consensus controller for homogeneous networked linear systems, maximizing the algebraic connectivity of a network by projected saddle point dynamics. In addition, the inverse optimal control problems for discrete-time finite time-horizon Linear Quadratic Regulators (LQRs) are considered. The goal is to infer the Q matrix in the quadratic cost function using the observations (possibly noisy) either on the optimal state trajectories, optimal control input or the system output.

    In Paper A, an optimal energy cost controller design for identical networked linear systems asymptotic consensus is considered. It is assumed that the topology of the network is given and the controller can only depend on relative information of the agents. Since finding the control gain for such a controller is hard, we focus on finding an optimal controller among a classical family of controllers which is based on the Algebraic Riccati Equation (ARE) and guarantees asymptotic consensus. We find that the energy cost is bounded by an interval and hence we minimize the upper bound. Further, the minimization for the upper bound boils down to optimizing the control gain and the edge weights of the graph separately. A suboptimal control gain is obtained by choosing Q=0 in the ARE. Negative edge weights are allowed, meaning that "competitions" between the agents are allowed. The edge weight optimization problem is formulated as a Semi-Definite Programming (SDP) problem. We show that the lowest control energy cost is reached when the graph is complete and with equal edge weights. Furthermore, two sufficient conditions for the existence of negative optimal edge weights realization are given. In addition, we provide a distributed way of solving the SDP problem when the graph topology is regular.

    In Paper B, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with computable projection operation on its tangent cone as well as equality constraints. We show that the projected dynamical system converges to one of the saddle points and hence finding an optimal solution. Moreover, the problem of distributedly maximizing the algebraic connectivity of an undirected network by optimizing the "port gains" of each nodes is considered. The original SDP problem is relaxed into a nonlinear programming (NP) problem that will be solved by the aforementioned projected dynamical system. Numerical examples show the convergence of the aforementioned algorithm to one of the optimal solutions. The effect of the relaxation is illustrated empirically with numerical examples. A methodology is presented so that the number of iterations needed to converge is reduced. Complexity per iteration of the algorithm is illustrated with numerical examples.

    In Paper C and D, the inverse optimal control problems over finite-time horizon for discrete-time LQRs are considered. The well-posedness of the inverse optimal control problem is first justified. In the noiseless case, when these observations of the optimal state trajectories or the optimal control input are exact, we analyze the identifiability of the problem and provide sufficient conditions for uniqueness of the solution. In the noisy case, when the observations are corrupted by additive zero-mean noise, we formulate the problem as an optimization problem and prove that the solution to this problem is statistically consistent. The following two scenarios are further considered: 1) the distributions of the initial state and the observation noise are unknown, yet the exact observations on the initial states and the noisy observations on the system output are available; 2) the exact observations on the initial states are not available, yet the observation noises are known to be white Gaussian and the distribution of the initial state is also Gaussian (with unknown mean and covariance). For the first scenario, we show statistical consistency for the estimation. For the second scenario, we fit the problem into the framework of maximum-likelihood and Expectation Maximization (EM) algorithm is used to solve this problem. The performance of the proposed method is illustrated through numerical examples.

  • 17. Fampa, Marcia
    et al.
    Luke, Daniela
    Wang, Fei
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Wolkowicz, Henry
    Parametric Convex Quadratic Relaxation of the Quadratic Knapsack Problem2019Inngår i: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 281, nr 1, s. 36-49Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a parametric convex quadratic programming (CQP) relaxation for the quadratic knapsack problem (QKP). This relaxation maintains partial quadratic information from the original QKP by perturbing the objective function to obtain a concave quadratic term. The nonconcave part generated by the perturbation is then linearized by a standard approach that lifts the problem to matrix space. We present a primal-dual interior point method to optimize the perturbation of the quadratic function, in a search for the tightest upper bound for the QKP. We prove that the same perturbation approach, when applied in the context of semidefinite programming (SDP) relaxations of the QKP, cannot improve the upper bound given by the corresponding linear SDP relaxation. The result also applies to more general integer quadratic problems. Finally, we propose new valid inequalities on the lifted matrix variable, derived from cover and knapsack inequalities for the QKP, and present separation problems to generate cuts for the current solution of the CQP relaxation. Our best bounds are obtained alternating between optimizing the parametric quadratic relaxation over the perturbation and applying cutting planes generated by the valid inequalities proposed.

  • 18.
    Oliveira, Rui Filipe De Sousa
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Lima, Pedro F.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Pereira, Goncalo Collares
    KTH, Skolan för industriell teknik och management (ITM), Centra, Integrated Transport Research Lab, ITRL. KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Mårtensson, Jonas
    KTH, Tidigare Institutioner (före 2005), Signaler, sensorer och system. KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Biomedicinsk fysik och röntgenfysik. KTH, Skolan för industriell teknik och management (ITM), Centra, Integrated Transport Research Lab, ITRL. KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Wahlberg, Bo
    KTH, Tidigare Institutioner (före 2005), Signaler, sensorer och system. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Path Planning for Autonomous Bus Driving in Highly Constrained Environments2019Inngår i: 2019 IEEE Intelligent Transportation Systems Conference (ITSC), 2019, s. 2743-2749Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Driving in urban environments often presents difficult situations that require expert maneuvering of a vehicle. These situations become even more challenging when considering large vehicles, such as buses. We present a path planning framework that addresses the demanding driving task of buses in highly constrained environments, such as urban areas. The approach is formulated as an optimization problem using the road-aligned vehicle model. The road-aligned frame introduces a distortion on the vehicle body and obstacles, motivating the development of novel approximations that capture this distortion. These approximations allow for the formulation of safe and accurate collision avoidance constraints. Unlike other path planning approaches, our method exploits curbs and other sweepable regions, which a bus must often sweep over in order to manage certain maneuvers. Furthermore, it takes full advantage of the particular characteristics of buses, namely the overhangs, an elevated part of the vehicle chassis, that can sweep over curbs. Simulations are presented, showing the applicability and benefits of the proposed method.

  • 19.
    Breiten, Tobias
    et al.
    Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität, Graz, 8010, Austria.
    Ringh, Emil
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Residual-based iterations for the generalized Lyapunov equation2019Inngår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 59, nr 4, s. 823-852Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper treats iterative solution methods for the generalized Lyapunov equation. Specifically, a residual-based generalized rational-Krylov-type subspace is proposed. Furthermore, the existing theoretical justification for the alternating linear scheme (ALS) is extended from the stable Lyapunov equation to the stable generalized Lyapunov equation. Further insights are gained by connecting the energy-norm minimization in ALS to the theory of H2-optimality of an associated bilinear control system. Moreover it is shown that the ALS-based iteration can be understood as iteratively constructing rank-1 model reduction subspaces for bilinear control systems associated with the residual. Similar to the ALS-based iteration, the fixed-point iteration can also be seen as a residual-based method minimizing an upper bound of the associated energy norm.

  • 20.
    Shariati, Nafiseh
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Teknisk informationsvetenskap.
    Zachariah, Dave
    Uppsala University.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Bengtsson, Mats
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Teknisk informationsvetenskap.
    Robust Optimal Power Distribution for Hyperthermia Cancer Treatment2019Inngår i: Medical Internet of Things (m-IoT) / [ed] Hamed Farhadi, IntechOpen , 2019, s. 55-70Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    We consider an optimization problem for spatial power distribution generated by an array of transmitting elements. Using ultrasound hyperthermia cancer treatment as a motivating example, the signal design problem consists of optimizing the power distribution across the tumor and healthy tissue regions, respectively. The models used in the optimization problem are, however, invariably subject to errors. To combat such unknown model errors, we formulate a robust signal design framework that can take the uncertainty into account using a worst-case approach. This leads to a semi-infinite programming (SIP) robust design problem, which we reformulate as a tractable convex problem that potentially has a wider range of applications.

  • 21. Ma, Shiqian
    et al.
    Wang, Fei
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Wei, Linchuan
    Wolkowicz, Henry
    Robust Principal Component Analysis using Facial Reduction2019Inngår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924Artikkel i tidsskrift (Fagfellevurdert)
  • 22.
    Yang, Bo
    et al.
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Hubei, Peoples R China..
    Cheng, Weizheng
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Hubei, Peoples R China..
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Zhu, Chao
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Hubei, Peoples R China..
    Yu, Xin
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Hubei, Peoples R China..
    Li, Xu
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Hubei, Peoples R China..
    Huang, Tao
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Hubei, Peoples R China..
    Seeking community structure in networks via biogeography-based optimization with consensus dynamics2019Inngår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 527, artikkel-id 121188Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Uncovering the community structure hidden in networks is crucial for understanding the function of networks. In this paper, an algorithm of biogeography-based optimization with consensus dynamics for community detection is proposed. The problems of seeking community structures in networks are exquisitely embedded into the framework of biogeography-based optimization. Hence the community structure unveiled in such an evolutionary and global manner is corresponding to the habitat with maximum modularity. We present a dynamical framework for generating initial distribution of solutions for the evolutionary process using consensus dynamics, which gives a reasonably good estimate of the community structure based on the topological information. Thereof, the proposed dynamical method of initialization promotes the efficiency of optimal solution search significantly, compared with the traditional random initialization. Then, the obtained partition is refined using biogeography-based optimization. In addition, a preferential selection strategy for generating the new solutions is developed based on local network topology. Furthermore, we also proposed an adaptive mutation operator that enhances the exploration ability of our evolutionary algorithm. The experimental results on both artificial random and real-world networks indicate the effectiveness and reliability of our algorithm. These findings shed new light on the role played by topological knowledge of networks extracted from consensus dynamics in the evolving optimization processes when finding complex mesoscale structures in networks such as community structure.

  • 23.
    Svensson, Göran
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Topics in Workforce Management in a Contact Center Context2019Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    This thesis is written as a monograph covering topics in operations research and focusing on workforce

    management in a contact center environment.

    This text is the result of a cooperative project between the Royal Institute of Technology (KTH) and

    Teleopti WFM.

    The main objective is to transform everyday problems faced at Teleopti into a mathematical

    modeling framework.

    The modeling aspect plays a prominent role and therefore, a large portion of this thesis deals with

    the modeling aspects of contact center management.

    The majority of the models are proposed in terms of Markov queuing networks.

    The text is divided into five chapters.

    The first chapter covers the introduction and provides a short background of

    the basics of contact centers and workforce management.

    It also briefly mentions the necessary mathematical tools.

    In Chapter 2, a multiclass and multiserver queuing network with a common budget constraint is introduced.

    The multiobjective optimization problem of minimizing server costs while delivering a high quality of service

    is solved using the marginal allocation algorithm.

    The quality of service measures used to quantify customer satisfaction is the conditional value-at-risk

    measure and the fraction of abandoning customers.

    It is proved that the conditional value-at-risk measure is integer convex in terms of the number of servers

    when the customer waiting time is taken as the loss function.

    In Chapter 3, the contact center interagent fairness is considered.

    The importance of agent happiness in face of attrition is briefly discussed.

    To include the interagent fairness into the modeling procedure a multiclass and multiserver queuing

    network is introduced.

    The servers are grouped into pools of exchangeable agents serving a subset of the customer classes.

    The interagent fairness measure can be introduced either as part of the objective function or as part

    of the optimization constraints.

    Robustness and multiperiod solutions are also considered.

    In Chapter 4, a limited state dependent server sharing system is considered in the context of

    a chat based communication system.

    The proposed model is an extension of the Markov queuing model applied to telephone based

    communication systems, where the agents may serve several customers concurrently.

    The service intensity provided depend on how many concurrent customers an agent serves which

    increases the complexity of the model.

    It is shown how agents of similar performance can be categorised together into groups and thus be handled separately.

    Several results pertaining to solving such a system are introduced and exemplified.

    In Chapter 5, the estimation of the parameters of the model presented in Chapter 4 is considered.

    This process is strongly data dependent, i.e., data driven, and a data classification system is proposed

    to the data available for the estimation.

    The chapter then proceeds to

    investigate frequentist and Bayesian strategies of parameter

    estimation under conditions of high and low resolution data

    Furthermore, the model in Chapter 4 is evaluated in terms of a real chat center data set.

  • 24.
    Böck, Michelle
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Toward Robust Optimization of Adaptive Radiation Therapy2019Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Adaptive radiation therapy is an evolving cancer treatment approach which relies on adapting the treatment plan in response to patient-specific interfractional geometric variations occurring during the fractionated treatment. If those variations are not addressed through adaptive replanning, the resulting treatment quality may be compromised.

    The purpose of this thesis is to introduce a conceptual framework that combines a variety of robust optimization approaches with the concept of adaptive radiation therapy. Robust optimization approaches are useful in radiation therapy, since interfractional geometric variations are accounted for while optimizing the treatment plan. Thus, combining these two concepts in a framework for robust adaptive radiation therapy gives the opportunity to optimize adapted robust plans which account for the actual interfractional variations in the individual case. In this thesis, a variety of frameworks with increasing complexity is introduced and their ability to handle interfractional variations is evaluated.

    In the first paper, a framework based on the concept of combining stochastic minimax optimization with adaptive replanning is introduced. Within this framework, three adaptive strategies are evaluated based on their ability to mitigate the impact of interfractional variations on the accumulated dose. In these strategies, treatment plans are adapted in response to the measured variations by (i) modifying the probability distribution that governs the variations accounted for in the optimization, (ii) varying the level of conservativeness of the robust optimization approach, and (iii) modifying safety-margins around the tumor.

    In the second paper, robust optimization approaches of varying levels of conservativeness are combined with optimization variables of varying degrees of freedom which account for fractionation and the interfractional geometric variations. The mathematical analysis shows that the solution of a time-independent problem is as good as the solution by the corresponding time-dependent problem, under the condition of convexity and independently and identically distributed interfractional geometric variations.

    In the third paper, the framework from the second paper is extended to (i) handle unaccounted interfractional geometric variations with Bayesian inference, (ii) address adaptation cost through varying the adaptation frequency, and (iii) address computational tractability of robust optimization approaches with an approximation algorithm.

    To emphasize the mathematical properties of the introduced frameworks, their performance is evaluated on an idealized one-dimensional phantom geometry subjected to a series of rigid translations. In this idealized phantom geometry, the relation between a modified optimization parameter and a feature in the resulting dose profile can be identified in a straightforward manner. This contributes to a better understanding of the underlying mechanisms between robustness, the adaptive strategies and the optimized dose profiles. The findings of this thesis are intended to provide a mathematical foundation for further development of the framework for, and research on, robust optimization of adaptive radiation therapy toward a clinical setting.

  • 25.
    Li, Yibei
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. Harbin Inst Technol, Harbin 150001, Heilongjiang, Peoples R China..
    Zhang, Han
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Yao, Yu
    Harbin Inst Technol, Harbin 150001, Heilongjiang, Peoples R China..
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A Convex Optimization Approach to Inverse Optimal Control2018Inngår i: 2018 37Th Chinese Control Conference, CCC (CCC) / [ed] Chen, X Zhao, QC, IEEE, 2018, Vol. 2018, s. 257-262Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, the problem of inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. In order to guarantee the feasibility of the problem, the IOC is reformulated as an infinite-dimensional convex optimization problem, which is then solved in the primal-dual framework. In addition, the feasibility of the original IOC could be determined from the optimal value of reformulated problem, which also gives out an approximate solution when the original problem is not feasible. In addition, several simplification methods are proposed to facilitate the computation, by which the problem is reduced to a boundary value problem of ordinary differential equations. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.

  • 26.
    Zhang, Silun
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A moment-based approach to modeling collective behaviors2018Inngår i: 2018 IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, s. 1681-1687, artikkel-id 8619389Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the occupation measure of the group of agents by their moments and show how the dynamics of the moments can be modeled. Then approximate trajectories of the moments can be computed and an inverse problem is solved to recover macro-scale properties of the group of agents. To illustrate the theory, a numerical example with interactions between the agents is given.

  • 27.
    Engberg, Lovisa
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Automated radiation therapy treatment planning by increased accuracy of optimization tools2018Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Every radiation therapy treatment is preceded by a treatment planning phase. In this phase, a treatment plan that specifies exactly how to irradiate the patient is designed by the treatment planner. Since the introduction of intensity-modulated radiation therapy into clinical practice in the 1990's, treatment planning involves, and requires, the use of advanced optimization tools due to the largely increased degrees of freedom in treatment specifications compared to earlier radiation therapy techniques.

    The aim of treatment planning is to create a plan that results in the, in some sense, best treatment---a treatment that at the same time reflects the patient-specific clinical goals, achieves the best possible quality, and adheres to other possible preferences of the oncologist or of the clinic. Despite dedicated treatment planning systems available with advanced optimization tools, treatment planning is often referred to as a complicated process involving many iterations with successively adjusted parameters. Over the years, a request has emerged from the clinical and treatment planners' side to make treatment planning less time-consuming and more straightforward, and the methods subsequently developed as a response have come to be referred to as methods for automated treatment planning.

    In this thesis, a framework for automated treatment planning is proposed and its potential and flexibility investigated. The focus is placed on increasing the accuracy of the optimization tools, aiming at achieving a less complicated treatment planning process that is driven by intuition rather than, as currently, trial and error. The suggested framework is contrasted to a class of methods dominating in the literature, which applies a more classical view of automation to treatment planning and strives towards reducing any type of human interaction. To increase the accuracy of the optimization tools, the underlying so-called objective functions are reformulated to better correlate with measures of treatment plan quality while possessing mathematical properties favorable for optimization. An important step is to show that the suggested framework not only is theoretically desirable, but also useful in practice. An interior-point method is therefore tailored to the specific structure of the novel optimization formulation, and is applied throughout the thesis, to demonstrate tractability. Numerical studies support the idea of the suggested framework equipping the treatment planner with more accurate and thereby less complicated tools to more straightforwardly handle the intrinsically complex process that constitutes treatment planning. 

  • 28.
    Zhang, Han
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Consensus control for linear systems with optimal energy cost2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 93, s. 83-91Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we design an optimal energy cost controller for linear systems asymptotic consensus given the topology of the graph. The controller depends only on relative information of the agents. Since finding the control gain for such controller is hard, we focus on finding an optimal controller among a classical family of controllers which is based on Algebraic Riccati Equation (ARE) and guarantees asymptotic consensus. Through analysis, we find that the energy cost is bounded by an interval and hence we minimize the upper bound. In order to do that, there are two classes of variables that need to be optimized: the control gain and the edge weights of the graph and are hence designed from two perspectives. A suboptimal control gain is obtained by choosing Q=0 in the ARE. Negative edge weights are allowed, and the problem is formulated as a Semi-definite Programming (SDP) problem. Having negative edge weights means that “competitions” between the agents are allowed. The motivation behind this setting is to have a better system performance. We provide a different proof compared to Thunberg and Hu (2016) from the angle of optimization and show that the lowest control energy cost is reached when the graph is complete and with equal edge weights. Furthermore, two sufficient conditions for the existence of negative optimal edge weights realization are given. In addition, we provide a distributed way of solving the SDP problem when the graph topology is regular.

  • 29.
    Deng, Juan
    et al.
    Chinese Acad Sci, Acad Math & Syst Sci, LSC, Beijing 100190, Peoples R China.;Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China..
    Wang, Lin
    Shanghai Jiao Tong Univ, Dept Automat, Shanghai 200240, Peoples R China.;Minist Educ, Key Lab Syst Control & Informat Proc, Shanghai 200240, Peoples R China..
    Liu, Zhixin
    Chinese Acad Sci, Acad Math & Syst Sci, LSC, Beijing 100190, Peoples R China.;Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China..
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Coordination of multiple rigid bodies under distance-induced interaction topologies2018Inngår i: IET Control Theory & Applications, ISSN 1751-8644, E-ISSN 1751-8652, Vol. 12, nr 15, s. 2067-2075Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This study considers the coordination control problem of a group of moving rigid bodies. Each rigid body communicates with other bodies via the distance-induced neighbour graphs. The authors design the distributed control laws for the angular velocity and linear velocity of rigid bodies, and establish sufficient conditions without relying on the dynamical properties of neighbour graphs, to guarantee that the rigid bodies reach the attitude synchronisation and avoid collision with nearby bodies while the communication networks keep connected. Moreover, they introduce a leader into the system to guide all rigid bodies to the desired attitude. Simulation examples are given to illustrate the authors' results.

  • 30.
    Wang, Lin
    et al.
    Shanghai Jiao Tong Univ, Dept Automat, Shanghai, Peoples R China.;Minist Educ, Key Lab Syst Control & Informat Proc, Shanghai, Peoples R China..
    Markdahl, Johan
    Univ Luxembourg, Luxembourg Ctr Syst Biomed, Esch Zur Alzette, Luxembourg..
    Liu, Zhixin
    Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing, Peoples R China..
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Decentralized cooperative tracking subject to motion constraints2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 96, s. 121-126Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper addresses the formation control problem, where three agents are tasked with moving an object cooperatively along a desired trajectory while also adjusting its posture to some desired attitudes, i.e. position and attitude tracking. Two decentralized control laws based on locally available information are proposed. The first control law maintains constant inter-agent distances over time, i.e. the formation of agents moves as a single rigid-body. The second control law relaxes this constraint by only maintaining similarity of the agent formation as a polygon in Euclidean space. 

  • 31.
    Zhang, Silun
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    He, Fenghua
    Control and Simulation Center, Harbin Institute of Technology, Harbin, 150001, P. R. China.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Exponential Stability of Formations for Reduced Attitudes: A Coordinates Free Approach2018Inngår i: Proceedings of Chinese Control Conference, 2018, IEEE Computer Society, 2018, s. 7220-, artikkel-id 7215Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work, a methodology based on differential geometry techniques is proposed to investigate exponential stability of a formation for reduced attitudes. By the proposed method, there is no need in finding any relative coordinates, which is typically needed but shown to be difficult when the formation problem is evolving in a non-Euclidean space. In this paper, the desired formation is treated as an embedding submanifold in (S-2)(N) and by using the rotation symmetries owned by the attitude dynamics its stability is directly examined. Moreover, such a method turns out to be coordinates free, namely, exponential stability of a formation can be completely determined by just investigating any one equilibrium which can result in the formation under any local chart of (S-2)(N). This greatly simplifies the stability analysis for the formation problems.

  • 32.
    Wei, Jieqiang
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Zhang, Silun
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Adaldo, Antonio
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Johan, Thunberg
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Finite-time attitude synchronization with distributed discontinuous protocols2018Inngår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, nr 10, s. 3608-3615Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper.

  • 33.
    Engberg, Lovisa
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. RaySearch Labs, Sveavagen 44, SE-10365 Stockholm, Sweden..
    Eriksson, Kjell
    RaySearch Labs, Sveavagen 44, SE-10365 Stockholm, Sweden..
    Forsgren, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Increased accuracy of planning tools for optimization of dynamic multileaf collimator delivery of radiotherapy through reformulated objective functions2018Inngår i: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 63, nr 12, artikkel-id 125012Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this study is to examine in a clinical setting a novel formulation of objective functions for intensity-modulated radiotherapy treatment plan multicriteria optimization (MCO) that we suggested in a recent study. The proposed objective functions are extended with dynamic multileaf collimator (DMLC) delivery constraints from the literature, and a tailored interior point method is described to efficiently solve the resulting optimization formulation. In a numerical planning study involving three patient cases, DMLC plans Pareto optimal to the MCO formulation with the proposed objective functions are generated. Evaluated based on pre-defined plan quality indices, these DMLC plans are compared to conventionally generated DMLC plans. Comparable or superior plan quality is observed. Supported by these results, the proposed objective functions are argued to have a potential to streamline the planning process, since they are designed to overcome the methodological shortcomings associated with the conventional penalty-based objective functions assumed to cause the current need for time-consuming trial-and-error parameter tuning. In particular, the increased accuracy of the planning tools imposed by the proposed objective functions has the potential to make the planning process less complicated. These conclusions position the proposed formulation as an alternative to existing methods for automated planning.

  • 34.
    Elvander, Filip
    et al.
    Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
    Jakobsson, Andreas
    Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport2018Inngår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, nr 20, s. 5285-5298Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semidefiniteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes.

  • 35.
    Zhang, Silun
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. Harbin Institute of Technology, China.
    Song, Wenjun
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    He, Fenghua
    Control and Simulation Center, Harbin Institute of Technology, 150001 Harbin, China.
    Hong, Yiguang
    Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Intrinsic tetrahedron formation of reduced attitude2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 87, s. 375-382Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, formation control for reduced attitude is studied, in which a regular tetrahedron formation can be achieved and shown to be asymptotically stable under a large family of gain functions in the control. Moreover, by further restriction on the control gain, almost global stability of the desired formation is obtained. In addition, the control proposed is an intrinsic protocol that only uses relative information and does not need to contain any information of the desired formation beforehand. The constructed formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Besides, a novel coordinates transformation is proposed to represent the relative reduced attitudes in S2, which is shown to be an efficient approach to reduced attitude formation problems.

  • 36.
    Ringh, Axel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Lindquist, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. Shanghai Jiao Tong Univ, Dept Automat, Shanghai, Peoples R China; Shanghai Jiao Tong Univ, Sch Math, Shanghai, Peoples R China.
    Lower bounds on the maximum delay margin by analytic interpolation2018Inngår i: 2018 IEEE 57th Annual Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, s. 5463-5469, artikkel-id 8618930Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We study the delay margin problem in the context of recent works by T. Qi, J. Zhu, and J. Chen, where a sufficient condition for the maximal delay margin is formulated in terms of an interpolation problem obtained after introducing a rational approximation. Instead we omit the approximation step and solve the same problem directly using techniques from function theory and analytic interpolation. Furthermore, we introduce a constant shift in the domain of the interpolation problem. In this way we are able to improve on their lower bound for the maximum delay margin.

  • 37.
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Multidimensional inverse problems in imaging and identification using low-complexity models, optimal mass transport, and machine learning2018Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis, which mainly consists of six appended papers, primarily considers a number of inverse problems in imaging and system identification.

    In particular, the first two papers generalize results for the rational covariance extension problem from one to higher dimensions. The rational covariance extension problem stems from system identification and can be formulated as a trigonometric moment problem, but with a complexity constraint on the sought measure. The papers investigate a solution method based on varia tional regularization and convex optimization. We prove the existence and uniqueness of a solution to the variational problem, both when enforcing exact moment matching and when considering two different versions of approximate moment matching. A number of related questions are also considered, such as well-posedness, and the theory is illustrated with a number of examples.

    The third paper considers the maximum delay margin problem in robust control: To find the largest time delay in a feedback loop for a linear dynamical system so that there still exists a single controller that stabilizes the system for all delays smaller than or equal to this time delay. A sufficient condition for robust stabilization is recast as an analytic interpolation problem, which leads to an algorithm for computing a lower bound on the maximum delay margin. The algorithm is based on bisection, where positive semi-definiteness of a Pick matrix is used as selection criteria.

    Paper four investigate the use of optimal transport as a regularizing functional to incorporate prior information in variational formulations for image reconstruction. This is done by observing that the so-called Sinkhorn iterations, which are used to solve large scale optimal transport problems, can be seen as coordinate ascent in a dual optimization problem. Using this, we extend the idea of Sinkhorn iterations and derive a iterative algorithm for computing the proximal operator. This allows us to solve large-scale convex optimization problems that include an optimal transport term.

    In paper five, optimal transport is used as a loss function in machine learning for inverse problems in imaging. This is motivated by noise in the training data which has a geometrical characteristic. We derive theoretical results that indicate that optimal transport is better at compensating for this type of noise, compared to the standard 2-norm, and the effect is demonstrated in a numerical experiment.

    The sixth paper considers using machine learning techniques for solving large-scale convex optimization problems. We first parametrizes a family of algorithms, from which a new optimization algorithm is derived. Then we apply machine learning techniques to learn optimal parameters for given families of optimization problems, while imposing a fixed number of iterations in the scheme. By constraining the parameters appropriately, this gives learned optimization algorithms with provable convergence.

  • 38.
    Ringh, Axel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Lindquist, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. Shanghai Jiao Tong University, China.
    Multidimensional rational covariance extension with approximate covariance matching2018Inngår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 56, nr 2, s. 913-944Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In our companion paper [A. Ringh, J. Karlsson, and A. Lindquist, SIAM T. Control Opton., 54 (2016), pp. 1950-1982] we discussed the multidimensional rational covariance extension problem (RCEP), which has important applications in image processing and spectral estimation in radar, sonar, and medical imaging. This is an inverse problem where a power spectrum with a rational absolutely continuous part is reconstructed from a finite set of moments. However, in most applications these moments are determined from observed data and are therefore only approximate, and the RCEP may not have a solution. In this paper we extend the results of our companion paper to handle approximate covariance matching. We consider two problems, one with a soft constraint and the other one with a hard constraint, and show that they are connected via a homeomorphism. We also demonstrate that the problems are well-posed and illustrate the theory by examples in spectral estimation and texture generation.

  • 39.
    Enqvist, Per
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Svensson, Göran
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. Teleopti WFM, Teleopti AB, Sweden.
    Multi-server marginal allocation With CVaR and abandonment based QoS measures2018Inngår i: ICORES 2018 - Proceedings of the 7th International Conference on Operations Research and Enterprise Systems, SciTePress, 2018, s. 297-303Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Two multi-objective minimization problems are posed, one for Erlang-C queues and one for Erlang-A queues. The objectives are to minimize the cost of added agents while also trying to optimize a quality of service measure. For the Erlang-C system we propose using the Conditional Value-at-Risk measure with waiting time as the loss function. We prove that this quality of service measure is integer convex in the number of servers. For the Erlang-A system we use the fraction of abandoning customers and some rate based weighting function as the service measure. Finally, a numerical comparison of the two system types is performed. The numerical results show the similarities between the two systems in terms of optimal points.

  • 40.
    Forsgren, Anders
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Odland, Tove
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    On exact linesearch quasi-Newton methods for minimizing a quadratic function2018Inngår i: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 69, nr 1, s. 225-241Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper concerns exact linesearch quasi-Newton methods for minimizing a quadratic function whose Hessian is positive definite. We show that by interpreting the method of conjugate gradients as a particular exact linesearch quasi-Newton method, necessary and sufficient conditions can be given for an exact linesearch quasi-Newton method to generate a search direction which is parallel to that of the method of conjugate gradients. We also analyze update matrices and give a complete description of the rank-one update matrices that give search direction parallel to those of the method of conjugate gradients. In particular, we characterize the family of such symmetric rank-one update matrices that preserve positive definiteness of the quasi-Newton matrix. This is in contrast to the classical symmetric-rank-one update where there is no freedom in choosing the matrix, and positive definiteness cannot be preserved. The analysis is extended to search directions that are parallel to those of the preconditioned method of conjugate gradients in a straightforward manner.

  • 41. Deng, Juan
    et al.
    Wang, Lin
    Liu, Zhixin
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Pose Synchronization of Multiple Rigid Bodies Under Average Dwell Time Condition2018Inngår i: Journal of Systems Science and Complexity, ISSN 1009-6124, E-ISSN 1559-7067, Vol. 31, nr 1, s. 215-233Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper considers the pose synchronization problem of a group of moving rigid bodies under switching topologies where the dwell time of each topology may has no nonzero lower bound. The authors introduce an average dwell time condition to characterize the length of time intervals in which the graphs are connected. By designing distributed control laws of angular velocity and linear velocity, the closed-loop dynamics of multiple rigid bodies with switching topologies can be converted into a hybrid dynamical system. The authors employ the Lyapunov stability theorem, and show that the pose synchronization can be reached under the average dwell time condition. Moreover, the authors investigate the pose synchronization problem of the leader-following model under a similar average dwell time condition. Simulation examples are given to illustrate the results.

  • 42. Lima, Pedro F.
    et al.
    Collares Pereira, Goncalo
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Mårtensson, Jonas
    KTH, Skolan för industriell teknik och management (ITM), Centra, Integrated Transport Research Lab, ITRL.
    Wahlberg, Bo
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Progress Maximization Model Predictive Controller2018Inngår i: 2018 21ST INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS (ITSC), IEEE , 2018, s. 1075-1082Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper addresses the problem of progress maximization (i.e., traveling time minimization) along a given path for autonomous vehicles. Progress maximization plays an important role not only in racing, but also in efficient and safe autonomous driving applications. The progress maximization problem is formulated as a model predictive controller, where the vehicle model is successively linearized at each time step, yielding a convex optimization problem. To ensure real-time feasibility, a kinematic vehicle model is used together with several linear approximations of the vehicle dynamics constraints. We propose a novel polytopic approximation of the 'g-g' diagram, which models the vehicle handling limits by constraining the lateral and longitudinal acceleration. Moreover, the tire slip angles are restricted to ensure that the tires of the vehicle always operate in their linear force region by limiting the lateral acceleration. We illustrate the effectiveness of the proposed controller in simulation, where a nonlinear dynamic vehicle model is controlled to maximize the progress along a track, taking into consideration possible obstacles.

  • 43.
    Hagrot, Erika
    et al.
    KTH, Skolan för bioteknologi (BIO), Industriell bioteknologi.
    Oddsdóttir, Hildur Æsa
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hosta, Joan Gonzalez
    KTH, Skolan för bioteknologi (BIO), Industriell bioteknologi.
    Jacobsen, Elling W.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Chotteau, Véronique
    KTH, Skolan för bioteknologi (BIO), Industriell bioteknologi.
    Retraction notice to “Poly-pathway model, a novel approach to simulate multiple metabolic states by reaction network-based model – Application to amino acid depletion in CHO cell culture” (Journal of Biotechnology (2016) 228 (37–39)(S0168165616301213)(10.1016/j.jbiotec.2016.03.015))2018Inngår i: Journal of Biotechnology, ISSN 0168-1656, E-ISSN 1873-4863, Vol. 265Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/our-business/policies/article-withdrawal). The authors of the paper wish to retract the paper due to the discovery of a calculation error in the processing of the raw data. The discovered error concerns the calculation of the specific uptake/secretion rates for several metabolites in one of the experimental conditions, i.e. glutamine omission (called Q0). In other words, in Figure 2, the variations of the metabolic fluxes for the condition Q0 are not correct. When this error is corrected, the resulting mathematical model changes (in particular for the results associated with Q0 conditions), several figures and tables are modified, and the interpretation of the fluxes in Q0 has to be slightly modified. Therefore the authors wish to retract the article. However, the error does not affect the modelling approach or the methodology presented in the article. Therefore, a revised version with the correct data has since been published: http://www.sciencedirect.com/science/article/pii/S0168165617302663. We apologize to the scientific community for the need to retract the article and the inconvenience caused.

  • 44.
    Ringh, Emil
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Mele, Giampaolo
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jarlebring, Elias
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Sylvester-based preconditioning for the waveguide eigenvalue problem2018Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 542, nr 1, s. 441-463Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a nonlinear eigenvalue problem (NEP) arising from absorbing boundary conditions in the study of a partial differential equation (PDE) describing a waveguide. We propose a new computational approach for this large-scale NEP based on residual inverse iteration (Resinv) with preconditioned iterative solves. Similar to many preconditioned iterative methods for discretized PDEs, this approach requires the construction of an accurate and efficient preconditioner. For the waveguide eigenvalue problem, the associated linear system can be formulated as a generalized Sylvester equation AX+XB+A1XB1+A2XB2+K(ring operator)X=C, where (ring operator) denotes the Hadamard product. The equation is approximated by a low-rank correction of a Sylvester equation, which we use as a preconditioner. The action of the preconditioner is efficiently computed by using the matrix equation version of the Sherman-Morrison-Woodbury (SMW) formula. We show how the preconditioner can be integrated into Resinv. The results are illustrated by applying the method to large-scale problems.

    Fulltekst tilgjengelig fra 2020-05-03 09:14
  • 45. Chen, Y.
    et al.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Georgiou, T. T.
    The role of the time-arrow in mean-square estimation of stochastic processes2018Inngår i: IEEE Control Systems Letters, ISSN 2475-1456, Vol. 2, nr 1, s. 85-90Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this letter is to point out a certain dichotomy between the information that the past and future values of a multivariate stochastic process carry about the present. More specifically, vector-valued, secondorder stochastic processes may be deterministic in one time-direction but not in the other. This phenomenon, which is absent in scalar-valued processes, is deeply rooted in the geometry of the shift-operator. The exposition and the examples we discuss are based on the work of Douglas, Shapiro, and Shields on cyclic vectors of the backward shift and relate to classical ideas going back to Wiener and Kolmogorov. We focus on rank-one stochastic processes for which we obtain an explicit characterization of all regular processes that are deterministic in the reverse timedirection. This letter builds on examples and the goal is to provide insights to a control engineering audience with interests in estimation theory and modeling of time-series.

  • 46.
    Oliveira, Rui Filipe De Sousa
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Lima, Pedro F.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Cirillo, M.
    Mårtensson, Jonas
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Wahlberg, Bo
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Trajectory Generation using Sharpness Continuous Dubins-like Paths with Applications in Control of Heavy-Duty Vehicles2018Inngår i: 2018 European Control Conference, ECC 2018, Institute of Electrical and Electronics Engineers Inc. , 2018, s. 935-940Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present a trajectory generation framework for control of wheeled vehicles under steering actuator constraints. The motivation is smooth driving of autonomous heavy-duty vehicles, which are characterized by slow actuator dynamics. In order to deal with the slow dynamics, we take into account rate and, additionally, torque limitations of the steering actuator directly. Previous methods only take into account limitations in the path curvature, which deals indirectly with steering rate limitations. We propose the new concept of Sharpness Continuous curves, which uses cubic curvature paths together with circular arcs to steer the vehicle. The obtained paths are characterized by a smooth and continuously differentiable steering angle profile. The final trajectories computed with our method provide low-level controllers with reference signals which are easier to track, resulting in improved performance. The smoothness of the obtained steering profiles also results in increased passenger comfort. The method is characterized by fast computation times. We detail possible path planning applications of the method, and conduct simulations that show its advantages and real-time capabilities.

  • 47.
    Elvander, Filip
    et al.
    Lund Univ, Div Math Stat, Lund, Sweden..
    Jakobsson, Andreas
    Lund Univ, Div Math Stat, Lund, Sweden..
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    USING OPTIMAL MASS TRANSPORT FOR TRACKING AND INTERPOLATION OF TOEPLITZ COVARIANCE MATRICES2018Inngår i: 2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2018, s. 4469-4473Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work, we propose a novel method for interpolation and extrapolation of Toeplitz structured covariance matrices. By considering a spectral representation of Toeplitz matrices, we use an optimal mass transport problem in the spectral domain in order to define a notion of distance between such matrices. The obtained optimal transport plan naturally induces a way of interpolating, as well as extrapolating, Toeplitz matrices. The constructed covariance matrix interpolants and extrapolants preserve the Toeplitz structure, as well as the positive semi-definiteness and the zeroth covariance of the original matrices. We demonstrate the proposed method's ability to model locally linear shifts of spectral power for slowly varying stochastic processes, illustrating the achievable performance using a simple tracking problem.

  • 48. Markdahl, Johan
    et al.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Wang, Lin
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A geodesic feedback law to decouple the full and reduced attitude2017Inngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 102, s. 32-41Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n - 1-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example.

  • 49.
    Wang, Fei
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Reid, Greg
    Wolkowicz, Henry
    An SDP-based method for the real radical ideal membership test2017Inngår i: Proceedings of the 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 86-93Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Let V be the set of real solutions of a system of multivariate polynomial equations with real coefficients. The real radical ideal (RRI) of V is the infinite set of multivariate polynomials that vanish on V. We give theoretical results that yield a finite step numerical algorithm for testing if a given polynomial is a member of this RRI. The paper exploits recent work that connects solution sets of such real polynomial systems with solution sets of semidefinite programming, SDP, problems involving moment matrices. We take advantage of an SDP technique called facial reduction. This technique regularizes our problem by projecting the feasible set onto the so-called minimal face. In addition, we use the Douglas-Rachford iterative approach which has advantages over traditional interior point methods for our application. If V has finitely many real solutions, then our method yields a finite set of polynomials in the form of a geometric involutive basis that are generators of the RRI and form an RRI membership test. In the case where the set V has real solution components of positive dimension, and given an input polynomial of degree d, our method can also decide RRI membership via a truncated geometric involutive basis of degree d. Examples are given to illustrate our approach and its advantages that remove multiplicities and sums of squares that cause illconditioning for real solutions of polynomial systems.

  • 50. Li, Y.
    et al.
    Yao, Y.
    He, F.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Autonomous control and target tracking algorithm design for a quadrotor2017Inngår i: 2017 36th Chinese Control Conference (CCC), IEEE Computer Society, 2017, s. 6749-6754, artikkel-id 8028422Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, the task of Mission 7 of International Aerial Robotics Competition (IARC) is investigated. The quadrotor is required to autonomously navigate in a GPS-denied environment, and accomplish physical interaction with ground moving targets. In order to estimate the position of the quadrotor, a multi-sensor-compensation based method is designed and individual measurement errors are compensated. Also an extended Kalman filer (EKF) is utilized for attitude estimation. To accomplish the target tracking task, a path planning algorithm is designed under the constraints of quadrotor dynamics, and consecutive waypoint setpoints are generated. Then lower-level cascaded PID controllers are adopted to track the command waypoint. Finally, simulation and experimental results show the effectiveness and feasibility of the proposed methods.

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