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  • 501.
    Zhang, Han
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Umenberger, Jack
    Department of Information Technology, Division of Systems and Control, Uppsala University.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Inverse Quadratic Optimal Control for Discrete-Time Linear SystemsManuscript (preprint) (Other academic)
    Abstract [en]

    In this paper, we consider the inverse optimal control problem for discrete-time Linear Quadratic Regulators (LQRs), 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 justied. In the noiseless case, when these observations are exact, we analyze the identiability 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.

  • 502.
    Adler, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Elekta, Box 7593, 103 93 Stockholm, Sweden.
    Ringh, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Learning to solve inverse problems using Wasserstein lossManuscript (preprint) (Other academic)
    Abstract [en]

    We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.

  • 503.
    Karlsson, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Georgiou, Tryphon T.
    Localization of power spectraArticle in journal (Other academic)
  • 504.
    Zhang, Silun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ringh, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Modeling collective behaviors: A moment-based approachManuscript (preprint) (Other academic)
    Abstract [en]

    Abstract—In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution 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 distribution of the agents. In the latter an inverse problem is solved in order to reconstruct a nominal distribution and to recover the macro-scale properties of the group of agents. The proposed method is applicable for several types of multi-agent systems, e.g., leader-follower systems. We derive error bounds for the moment trajectories and describe how to take these error bounds into account for computing the moment dynamics. The convergence of the moment dynamics is also analyzed for cases with monomial moments. To illustrate the theory, two numerical examples are given. In the first we consider a multi-agent system with interactions and compare the proposed methods for several types of moments. In the second example we apply the framework to a leader-follower problem for modeling pedestrian crowd dynamics.

  • 505.
    Ringh, Axel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, Superseded Departments (pre-2005), Mathematics. Department of Automation, Shanghai Jiao Tong University, Shanghai, China.
    Multidimensional rational covariance extensionManuscript (preprint) (Other academic)
    Abstract [en]

    The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental theoretical questions. In fact, this inverse problem is a key component in many identification and signal processing techniques and plays a fundamental role in prediction, analysis, and modeling of systems and signals. It is well-known that the RCEP can be reformulated as a (truncated) trigonometric moment problem subject to a rationality condition. In this paper we consider the more general multidimensional trigonometric moment problem with a similar rationality constraint. This generalization creates many interesting new mathematical questions and also provides new insights into the original one-dimensional problem. A key concept in this approach is the complete smooth parametrization of all solutions, allowing solutions to be tuned to satisfy additional design specifications without violating the complexity constraints. As an illustration of the potential of this approach we apply our results to multidimensional spectral estimation, Wiener system identification, and image compression.

  • 506.
    Böck, Michelle
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On Adaptation Cost and Tractability in Robust Adaptive Radiation Therapy OptimizationManuscript (preprint) (Other academic)
    Abstract [en]

    A framework for online robust adaptive radiation therapy (ART) is presented. This framework is designed to (i) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (ii) address adaptation cost and (iii) address computational tractability. The novelty of this framework is the use of Bayesian inference and scenario-reduction, which is evaluated in a series of treatment on a one-dimensional phantom geometry. The initial robust plan is generated from a robust optimization problem based on either expected-value- or worst-case-optimization approach using the a priori hypothesis of the probability distribution governing the interfractional geometric variations. The actual interfractional variations are evaluated in terms of their likelihood with respect to the a priori hypothesis and violation of user-specified tolerance limits. During an adaptation the a posteriori distribution is computed from the actual variations using Bayesian inference. The adapted plan is optimized to better suit the actual interfractional variations of the individual case, which is used until the next adaptation is. To address adaptation cost, the proposed framework provides an option for increased adaptation frequency. Computational tractability is addressed by scenario-reduction algorithms to reduce the size of the optimization problem.  According to the simulations, the proposed framework may improve target coverage compared to the corresponding non-adaptive robust approach. Combining the worst-case-optimization approach with Bayesian inference may perform best in terms of improving CTV coverage and organ-at-risk~(OAR) protection. Bayesian inference may have a greater impact on handling adaptation cost than increased adaptation frequency. The concept of scenario-reduction may be useful to address computational tractability in ART and robust planning.

  • 507.
    Oddsdóttir, Hildur Æsa
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hagrot, Erika
    KTH, School of Biotechnology (BIO), Industrial Biotechnology.
    Chotteau, Veronique
    KTH, School of Biotechnology (BIO), Industrial Biotechnology.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On dynamically identifying elementary flux modes for a poly-pathway model of metabolic reaction networksManuscript (preprint) (Other academic)
    Abstract [en]

    he aim with poly-pathway models is to model variations in the metabolic behavior of cells in response to changes in their external environment.By considering the elementary flux modes of a metabolic network, the network can be reduced to a set of macroscopic reactions. The macroscopic reactions connect external substrates to products, where each reaction is associated with a kinetic equation.Since enumerating all elementary flux modes is prohibitive for complex networks, these types of models are usually limited to simple networks. In this work we consider an algorithm for identifying elementary flux modes for a poly-pathway model. First we consider a dynamic identification of elementary flux modes and model parameters using column generation. However, due to non-linearity in one optimization problem involved in column generation, elementary flux mode identification can not be guaranteed with that column generation approach. In order to still be able to identify elementary flux modes, an approximation algorithm is derived and tested for the model identification. In a case study, the algorithm is shown to work well in practice and obtains a near-optimal solution compared to a method in which all elementary flux modes are enumerated beforehand.

  • 508.
    Forsgren, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Odland, Tove
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On solving symmetric systems of linear equations in an unnormalized Krylov subspace frameworkArticle in journal (Other academic)
    Abstract [en]

    In an unnormalized Krylov subspace framework for solving symmetric systems of linear equations, the orthogonal vectors that are generated by a Lanczos process are not necessarily on the form of gradients. Associating each orthogonal vector with a triple, and using only the three-term recurrences of the triples, we give conditions on whether a symmetric system of linear equations is compatible or incompatible. In the compatible case, a solution is given and in the incompatible case, a certificate of incompatibility is obtained. In particular, the case when the matrix is singular is handled.

    We also derive a minimum-residual method based on this framework and show how the iterates may be updated explicitly based on the triples, and in the incompatible case a minimum-residual solution of minimum Euclidean norm is obtained.

  • 509.
    Fallgren, Mikael
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On the Complexity of Maximizing the Minimum Shannon Capacity by Joint Cell, Channel and Power Allocation in Wireless Communication NetworksManuscript (preprint) (Other academic)
    Abstract [en]

    We consider wireless telecommunications systems with orthogonal frequency bands, where each band is referred to as a channel, e.g., Orthogonal Frequency-Division Multiple Access (OFDMA). For a given snap-shot in time, the joint cell, channel and power allocation optimization problem is presented, both in downlink and in uplink. The objective is to maximize the minimum total Shannon capacity of any mobile user in the system, subject to system constraints. The corresponding decision problems are proved to be NP-hard. We also show that for any constant ρ > 0, a sufficiently large number of channels ensure that the optimization problems are not ρ-approximable, unless P is equal to NP. Furthermore, we show that the inapproximability property remains when solely considering the power allocation problem, i.e., given a feasible cell and channel allocation. This power allocation optimization problem is not convex in general, but in the simplified setting where each transmitter is allowed to use only one single channel, there exists known approaches to attain the global optimum. In this setting, we prove that any solution that fulfills the KKT conditions is a global optimum.

  • 510.
    Forsgren, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Odland, Tove
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On the equivalence of the method of conjugate gradients and quasi-Newton methods on quadratic problemsIn: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894Article in journal (Other academic)
    Abstract [en]

    In this paper we state necessary and sufficient conditions for equivalence of the method of conjugate gradients and quasi-Newton methods on a quadratic problem. We show that the set of quasi-Newton schemes that generate parallel search directions to those of the method of conjugate gradients is strictly larger than the one-parameter Broyden family. In addition, we show that this set contains an infinite number of symmetric rank-one update schemes.

  • 511.
    Oddsdóttir, Hildur Æsa
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hagrot, Erika
    KTH, School of Biotechnology (BIO), Industrial Biotechnology.
    Chotteau, Veronique
    KTH, School of Biotechnology (BIO), Industrial Biotechnology.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On the Robustness of Elementary-Flux-Modes-based Metabolic Flux AnalysisManuscript (preprint) (Other academic)
    Abstract [en]

    Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux measurements through least-squares data fitting. The measurements used in the data fitting are subject to errors. A robust optimization problem includes information on errors and gives a way to examine the sensitivity of the solution of the EFMs-based MFA to these errors. In general, formulating a robust optimization problem may make the problem significantly harder. We show that in the case of the EFMs-based MFA the robust problem can be stated as a convex quadratic programming problem. We have previously shown how the data fitting problem may be solved in a column-generation framework. In this paper, we show how column generation may be applied also to the robust problem. Furthermore, the option to indicate intervals on metabolites that are not measured is introduced in this column generation framework. The robustness of the data is evaluated in a case-study, which indicated that the solutions of our non-robust problems are in fact near-optimal also when robustness is considered, implying that the errors in measurement do not have a large impact on the optimal solution. Furthermore, we showed that the addition of intervals on unmeasured metabolites resulted in a change in the optimal solution.

  • 512.
    Engberg, Lovisa
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On tradeoffs between treatment time and plan quality of volumetric-modulated arc therapy with sliding-window deliveryIn: Article in journal (Other academic)
    Abstract [en]

    The purpose of this study is to give an exact formulation of optimization of volumetric-modulated arc therapy (VMAT) with sliding-window delivery, and to investigate the plan quality effects of decreasing the number of slidingwindow sweeps made on the 360-degree arc for a faster VMAT treatment. In light of the exact formulation, we interpret an algorithm previously suggested in the literature as a heuristic method for solving this optimization problem. By first making a generalization, we suggest a modification of this algorithm for better handling of plans with fewer sweeps. In a numerical study involving one prostate and one lung case, plans with varying treatment times and number of sweeps are generated. It is observed that, as the treatment time restrictions become tighter, fewer sweeps may lead to better plan quality. Performance of the original and the modified version of the algorithm is evaluated in parallel. Applying the modified version results in better objective function values and less dose discrepancies between optimized and accurate dose, and the advantages are pronounced with decreasing number of sweeps.

  • 513.
    Anisi, David
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Robinson, John W.C.
    Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.
    Ögren, Petter
    Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.
    Online Trajectory Planning for Aerial Vehicle: A Safe Approach with Guaranteed Task CompletionManuscript (Other academic)
    Abstract [en]

    On-line trajectory optimization in three dimensional space is the main topic of the paper at hand. The high-level framework augments on-line receding horizon control with an off-line computed terminal cost that captures the global characteristics of the environment, as well as any possible mission objectives. The first part of the paper is devoted to the single vehicle case while the second part considers the problem of simultaneous arrival of multiple aerial vehicles. The main contribution of the first part is two-fold. Firstly, by augmenting a so called safety maneuver at the end of the planned trajectory, this paper extends previous results by addressing provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method presented is shown to have finite time task completion. Moreover, a quantitative comparison between the two competing objectives of optimality and computational tractability is made. Finally, some other key characteristics of the trajectory planner, such as ability to minimize threat exposure and robustness, are highlighted through simulations. As for the simultaneous arrival problem considered in the second part, by using a time-scale separation principle, we are able to adopt standard Laplacian control to a consensus problem which is neither unconstrained, nor first order. 

  • 514.
    Karasalo, Maja
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Martin, Cylde
    Periodic and Recursive Control Theoretic Smoothing SplinesManuscript (preprint) (Other academic)
    Abstract [en]

    In this paper, a recursive control theoretic smoothing spline approach is proposed forreconstructing a closed contour.Periodic splines are generated by minimizing a cost function subjectto constraints imposed by a linear control system. The optimal controlproblem is shown to be proper, andsufficient optimality conditions are derived for a special case of the problem using Hamilton-Jacobi-Bellman theory.

    The filtering effect of the smoothing splines allows for usageof noisy sensor data. An important feature of the method is thatseveral data sets for the same closed contour can be processedrecursively so that the accuracy is improved stepwiseas new data becomes available.

  • 515.
    Hagrot, Erika
    et al.
    KTH, School of Biotechnology (BIO), Industrial Biotechnology.
    Oddsdóttir, Hildur Æsa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hosta, Joan Gonzalez
    Jacobsen, Elling W.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Chotteau, Veronique
    KTH, School of Biotechnology (BIO), Industrial Biotechnology.
    Poly-pathway model, a novel approach to simulate multiple metabolic states by reaction network-based model - Application to CHO cell cultureManuscript (preprint) (Other academic)
  • 516.
    Gustavi, Tove
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Robust tracking control and obstacle avoidance for non-holonomic mobile agentsManuscript (preprint) (Other academic)
    Abstract [en]

    Mobile robotics is a subfield of robotics that has received much attention in the last decades and the problem of tracking a moving object has been considered in many different settings. In this paper we consider a unicycle robot with non-holonomic motion constraints that tracks a target, using only local information. The presence of non-holonomic constraints is a complicating factor that is often deliberately overlooked in theoretical work. Still, for the results to be directly implementable, the non-holonomic constraints must be taken into account. In the paper, two types of decentralized tracking control algorithms, which do not require global information about the system, are proposed. Robustness to measurement noise is demonstrated in simulations and, in addition, a reactive obstacle avoidance control that can easily be integrated with the tracking functions is suggested.

  • 517.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sampled data control of DC-DC convertersArticle in journal (Other academic)
  • 518.
    Svärd, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Using the weakest link model of fatigue in topology optimizationManuscript (preprint) (Other academic)
    Abstract [en]

    In this work, a method for incorporating fatigue failure in topology op- timization problems is presented. The method is based on the weakest link model of failure, developed by Weibull. The model is based on an assumption on the failure probability of a volume element, as a function of the applied stress. Given some assumptions, the total failure probability of the structure may be calculated as an integral over all elements. In this paper, it is shown that the weakest link model for failure takes a form that is very suitable for topology optimization. In fact, it is shown that the expression for failure probability according to Weibull under some circumstances is very similar to the much used p-norm of stresses. In the paper, the weakest link model is explained in detail, and adaptations to make it suitable for topology optimization are made. Suggestions on how to choose the parameters of the model are given, and the effects of different parameter choices are evaluated using examples. 

891011 501 - 518 of 518
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