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  • 51.
    Zhang, Han
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Li, Yibei
    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.
    Discrete-Time Inverse Linear Quadratic Optimal Control over Finite Time-Horizon under Noisy Output Measurements2021In: Control Theory and Technology, ISSN 2095-6983, Vol. 19, no 4, p. 563-572Article in journal (Refereed)
    Abstract [en]

    In this paper, the problem of inverse quadratic optimal control over finite time-horizon for discrete-time linear systems is considered. Our goal is to recover the corresponding quadratic objective function using noisy observations. First, the identifiability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifiable. Next, we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown, yet the exact observations on the initial states are available. We formulate the problem as a risk minimization problem and approximate the problem using empirical average. It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees. We then study the case where the exact observations on the initial states are not available, yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian (with unknown mean and covariance). EM-algorihm is used to estimate the parameters in the objective function. The effectiveness of our results are demonstrated by numerical examples.

  • 52.
    Ringh, Axel
    et al.
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China..
    Haasler, Isabel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Chen, Yongxin
    Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Efficient computations of multi-species mean field games via graph-structured optimal transport2021In: Proceedings 2021 60th IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE) , 2021, p. 5261-5268Conference paper (Refereed)
    Abstract [en]

    In this work we develop an efficient numerical solution method for solving potential mean field games with multiple species. This is done by using recent developments that connect mean field games and entropy-regularized optimal transport. In particular, we reformulate the original problem as a structured entropy-regularized multi-marginal optimal transport problem, and develop highly efficient methods for solving the latter. Finally, we illustrate the proposed method on a problem with four interacting species, where each of the species has different target objectives.

  • 53.
    Özkahraman, Özer
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Robotics, Perception and Learning, RPL.
    Ögren, Petter
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Robotics, Perception and Learning, RPL.
    Efficient Navigation Aware Seabed Coverage using AUVs2021In: Proceedings of 2021 IEEE International Conference on Safety, Security, and Rescue Robotics (SSRR), October 25-27 2021, New York, USA., 2021Conference paper (Refereed)
    Abstract [en]

    Area coverage and robot navigation are two  important research fields within robotics. However, their intersection has received limited attention. In coverage problems, perfect navigation is often assumed, and in robot navigation, the focus is often to minimize the localization error while traveling a given trajectory.The need for integration of the two becomes clear in environments with very sparse features or landmarks, for example when an Autonomous Underwater Vehicle (AUV) is to search the seafloor for dangerous objects, such as mines.The potential consequences of missing a mine due to navigation errors can be catastrophic.If the localization error is large, a trajectory that was designed to guarantee complete coverage might have missed significant parts of the area. Thus, the coverage trajectory must be planned with the navigation performance in mind, applying a combination of using large enough planned overlaps of sensor footprints to account for the position uncertainty, and reducing this uncertainty by re-visiting the known sparse landmarks.

    In this paper we compute trajectories that guarantee coverage for a given area under assumptions on worst case localization error growth.We further more compute upper bounds for how large areas can be covered using common coverage patterns and a single landmark, which leads to bounds on how sparse the landmarks can be in the regions to be covered.

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  • 54.
    Ek, David
    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.
    Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function2021In: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 79, no 3, p. 789-816Article in journal (Refereed)
    Abstract [en]

    The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel to those of the BFGS method, or equivalently, to those of the method of preconditioned conjugate gradients. In the setting of reduced Hessians, the class provides a dynamical framework for the construction of limited-memory quasi-Newton methods. These methods attain finite termination on quadratic optimization problems in exact arithmetic. We show performance of the methods within this framework in finite precision arithmetic by numerical simulations on sequences of related systems of linear equations, which originate from the CUTEst test collection. In addition, we give a compact representation of the Hessian approximations in the full Broyden class for the general unconstrained optimization problem. This representation consists of explicit matrices and gradients only as vector components.

  • 55.
    Peng, Shen
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lisser, Abdel
    Laboratory of Signals and Systems, CentraleSupelec, Bat Breguet, 3 Rue Joliot Curie, 91190, Gif-sur-Yvette, France.
    Singh, Vikas Vikram
    Department of Mathematics, IIT Delhi, New Delhi, India.
    Gupta, Nalin
    Department of Mathematics, IIT Delhi, New Delhi, India.
    Balachandar, Eshan
    Department of Mathematics, IIT Delhi, New Delhi, India.
    Games with distributionally robust joint chance constraints2021In: Optimization Letters, ISSN 1862-4472, E-ISSN 1862-4480Article in journal (Refereed)
    Abstract [en]

    This paper studies an n-player non-cooperative game where each player has expected-value payoff function and chance-constrained strategy set. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong to a certain distributional uncertainty set. The chance-constrained strategy sets are defined using a distributionally robust framework. We consider one density based uncertainty set and four two-moments based uncertainty sets. One of the considered uncertainty sets is based on a nonnegative support. Under the standard assumptions on the players’ payoff functions, we show that there exists a Nash equilibrium of a distributionally robust chance-constrained game for each uncertainty set. As an application, we study Cournot competition in electricity market and perform the numerical experiments for the case of two electricity firms.

  • 56.
    Lourenço, Inês
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Mattila, Robert
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wahlberg, Bo
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hidden Markov Models: Inverse Filtering, Belief Estimation and Privacy Protection2021In: Journal of Systems Science and Complexity, ISSN 1009-6124, E-ISSN 1559-7067, Vol. 34, no 5, p. 1801-1820Article in journal (Refereed)
    Abstract [en]

    A hidden Markov model (HMM) comprises a state with Markovian dynamics that can only be observed via noisy sensors. This paper considers three problems connected to HMMs, namely, inverse filtering, belief estimation from actions, and privacy enforcement in such a context. First, the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter. Next, the authors consider a rational decision-maker that forms a private belief (posterior distribution) on the state of the world by filtering private information. The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent. In the setting of adversarial systems, the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions. Applications range from financial portfolio investments to life science decision systems.

  • 57.
    Li, Yibei
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wahlberg, Bo
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Identifiability and Solvability in Inverse Linear Quadratic Optimal Control Problems2021In: Journal of Systems Science and Complexity, ISSN 1009-6124, E-ISSN 1559-7067, Vol. 34, no 5, p. 1840-1857Article in journal (Refereed)
    Abstract [en]

    In this paper, the inverse linear quadratic (LQ) problem over finite time-horizon is studied. Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods.

  • 58. Singh, R.
    et al.
    Haasler, Isabel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Zhang, Q.
    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.
    Chen, Y.
    Incremental Inference of Collective Graphical Models2021In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 5, no 2, p. 421-426, article id 9119078Article in journal (Refereed)
    Abstract [en]

    We consider incremental inference problems from aggregate data for collective dynamics. In particular, we address the problem of estimating the aggregate marginals of a Markov chain from noisy aggregate observations in an incremental (online) fashion. We propose a sliding window Sinkhorn belief propagation (SW-SBP) algorithm that utilizes a sliding window filter of the most recent noisy aggregate observations along with encoded information from discarded observations. Our algorithm is built upon the recently proposed multi-marginal optimal transport based SBP algorithm that leverages standard belief propagation and Sinkhorn algorithm to solve inference problems from aggregate data. We demonstrate the performance of our algorithm on applications such as inferring population flow from aggregate observations.

  • 59.
    Winqvist, Rebecka
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Venkitaraman, Arun
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Wahlberg, Bo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Learning Models of Model Predictive Controllers using Gradient Data2021In: IFAC PAPERSONLINE, Elsevier BV , 2021, Vol. 54, no 7, p. 7-12Conference paper (Refereed)
    Abstract [en]

    This paper investigates the problem of controller identification given the data from a linear quadratic Model Predictive Controller (MPC) with constraints. We propose an approach for learning MPC that explicitly uses the gradient information in the training process. This is motivated by the observation that recent differentiable convex optimization MPC solvers can provide both the optimal feedback law from the state to control input as well as the corresponding gradient. As a proof of concept, we apply this approach to explicit MPC (eMPC), for which the feedback law is a piece-wise affine function of the state, but the number of pieces grows rapidly with the state dimension. Controller identification can here be used to find an approximate low complexity functional approximation of the controller. The eMPC is modelled using a Neural Network (NN) with Rectified Linear Units (ReLUs), since such NNs can represent any piece-wise affine function. A key motivation is to replace on-line solvers with neural networks to implement MPC and to simplify the evaluation of the function in larger input dimensions. We also study experimental design and model evaluation in this framework, and propose a hit-and-run sampling algorithm for input design. The proposed algorithms are illustrated and numerically evaluated on a second order MPC problem.

  • 60.
    Egidio, Lucas N.
    et al.
    Catholic Univ Louvain, ICTEAM, INMA, B-1348 Louvain La Neuve, Belgium..
    Hansson, Anders
    Linköping Univ, Dept Elect Engn, S-58183 Linköping, Sweden..
    Wahlberg, Bo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Learning the Step-size Policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno Algorithm2021In: 2021 international joint conference on neural networks (IJCNN), Institute of Electrical and Electronics Engineers (IEEE) , 2021Conference paper (Refereed)
    Abstract [en]

    We consider the problem to learn a step-size policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. This is a limited computational memory quasi-Newton method widely used for deterministic unconstrained optimization. However, L-BFGS is currently avoided in large-scale problems for requiring step sizes to be provided at each iteration. Current methodologies for the step size selection for L-BFGS use heuristic tuning of design parameters and massive re-evaluations of the objective function and gradient to find appropriate step-lengths. We propose a neural network architecture with local information of the current iterate as the input. The step-length policy is learned from data of similar optimization problems, avoids additional evaluations of the objective function, and guarantees that the output step remains inside a pre-defined interval. The corresponding training procedure is formulated as a stochastic optimization problem using the backpropagation through time algorithm. The performance of the proposed method is evaluated on the training of image classifiers for the MNIST database for handwritten digits and for CIFAR-10. The results show that the proposed algorithm outperforms heuristically tuned optimizers such as ADAM, RMSprop, L-BFGS with a backtracking line search, and L-BFGS with a constant step size. The numerical results also show that a learned policy can be used as a warm-start to train new policies for different problems after a few additional training steps, highlighting its potential use in multiple large-scale optimization problems.

  • 61.
    Zhu, Bin
    et al.
    Sun Yat Sen Univ, Sch Intelligent Syst Engn, Waihuan East Rd 132, Guangzhou 510006, Peoples R China..
    Ferrante, Augusto
    Univ Padua, Dept Informat Engn, Via Gradenigo 6-B, I-35131 Padua, Italy..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Zorzi, Mattia
    Univ Padua, Dept Informat Engn, Via Gradenigo 6-B, I-35131 Padua, Italy..
    M-2 SPECTRAL ESTIMATION: A FLEXIBLE APPROACH ENSURING RATIONAL SOLUTIONS2021In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 59, no 4, p. 2977-2996Article in journal (Refereed)
    Abstract [en]

    This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M-2. The problem is posed as solving a finite number of trigonometric moment equations for a nonnegative matricial measure, which is well known as the covariance extension problem in the literature of systems and control. This inverse problem and its various generalizations have been extensively studied in the past three decades, and they find applications in diverse fields such as modeling and system identification, signal and image processing, robust control, circuit theory, etc. In this paper, we address the challenging M-2 version of the problem, and elaborate on a solution technique via convex optimization with the tau-divergence family. As a major contribution of this work, we show that by properly choosing the parameter of the divergence index, the optimal spectrum is a rational function, that is, the solution is a spectral density which can be represented by a finite-dimensional system, as desired in many practical applications.

  • 62.
    Zhu, Bin
    et al.
    School of Intelligent Systems Engineering, Sun Yat-sen University, Waihuan East Road 132, 510006 Guangzhou, China.
    Ferrante, Augusto
    Department of Information Engineering, University of Padova, Via Gradenigo 6/B, 35131 Padova, Italy.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Zorzi, Mattia
    Department of Information Engineering, University of Padova, Via Gradenigo 6/B, 35131 Padova, Italy.
    M2-spectral estimation: A relative entropy approach2021In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 125, article id 109404Article in journal (Refereed)
    Abstract [en]

    This paper deals with M2-signals, namely multivariate (or vector-valued) signals defined over a multidimensional domain. In particular, we propose an optimization technique to solve the covariance extension problem for stationary random vector fields. The multidimensional Itakura–Saito distance is employed as an optimization criterion to select the solution among the spectra satisfying a finite number of moment constraints. In order to avoid technicalities that may happen on the boundary of the feasible set, we deal with the discrete version of the problem where the multidimensional integrals are approximated by Riemann sums. The spectrum solution is also discrete, which occurs naturally when the underlying random field is periodic. We show that a solution to the discrete problem exists, is unique and depends smoothly on the problem data. Therefore, we have a well-posed problem whose solution can be tuned in a smooth manner. Finally, we have applied our theory to the target parameter estimation problem in an integrated system of automotive modules. Simulation results show that our spectral estimator has promising performance. 

  • 63.
    Zhang, Silun
    et al.
    MIT, MIT Lab Informat & Decis Syst LIDS, 77 Massachusetts Ave, Cambridge, MA 02139 USA..
    Ringh, Axel
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Hong Kong, Peoples R China..
    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.
    Modeling Collective Behaviors: A Moment-Based Approach2021In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 66, no 1, p. 33-48Article in journal (Refereed)
    Abstract [en]

    In this article 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 macroscale properties of the group of agents. The proposed method is applicable for several types of multiagent 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 multiagent system with interactions and compare the proposed method for several types of moments. In the second example we apply the framework to a leader-follower problem for modeling a pedestrian crowd.

  • 64.
    Haasler, Isabel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ringh, Axel
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Clear Water Bay, Kowloon, Hong Kong, Peoples R China..
    Chen, Yongxin
    Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Multimarginal optimal transport with a tree-structured cost and the schrödinger bridge problem2021In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 59, no 4, p. 2428-2453Article in journal (Refereed)
    Abstract [en]

    The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the problem with an entropy term, which connects it to the Schrodinger bridge problem and thus to stochastic optimal control. Moreover, the entropy regularization makes the otherwise computationally demanding optimal transport problem feasible even for large scale settings. This has led to an accelerated development of optimal transport based methods in a broad range of fields. Many of these applications have an underlying graph structure, for instance, information fusion and tracking problems can be described by trees. In this work we consider multimarginal optimal transport problems with a cost function that decouples according to a tree structure. The entropy regularized multimarginal optimal transport problem can be viewed as a generalization of the Schrodinger bridge problem with the same tree-structure, and by utilizing these connections we extend the computational methods for the classical optimal transport problem in order to solve structured multimarginal optimal transport problems in an efficient manner. In particular, the algorithm requires only matrix-vector multiplications of relatively small dimensions. We show that the multimarginal regularization introduces less diffusion, compared to the commonly used pairwise regularization, and is therefore more suitable for many applications. Numerical examples illustrate this, and we finally apply the proposed framework for the tracking of an ensemble of indistinguishable agents.

  • 65.
    Ringh, Emil
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Jarlebring, Elias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Nonlinearizing two-parameter eigenvalue problems2021In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 42, no 2, p. 775-799Article in journal (Refereed)
    Abstract [en]

    We investigate a technique to transform a linear two-parameter eigenvalue problem, into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by considering it as a (standard) generalized eigenvalue problem. We characterize the equivalence between the original and the nonlinearized problem theoretically and show how to use the transformation computationally. Special cases of the transformation can be interpreted as a reversed companion linearization for polynomial eigenvalue problems, as well as a reversed (less known) linearization technique for certain algebraic eigenvalue problems with square-root terms. Moreover, by exploiting the structure of the NEP we present algorithm specializations for NEP-methods, although the technique also allows general solution methods for NEPs to be directly applied. The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller size than the other two-parameter eigenvalue equation. This situation arises naturally in domain decomposition techniques. A general error analysis is also carried out under the assumption that a backward stable eigensolver is used to solve the eliminated problem, leading to the conclusion that the error is benign in this situation.

  • 66.
    Ringh, Emil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Numerical methods for Sylvester-type matrix equations and nonlinear eigenvalue problems2021Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Linear matrix equations and nonlinear eigenvalue problems (NEP) appear in a wide variety of applications in science and engineering. Important special cases of the former are the Lyapunov equation, the Sylvester equation, and their respective generalizations. These appear, e.g., as Gramians to linear and bilinear systems, in computations involving block-triangularization of matrices, and in connection with discretizations of some partial differential equations. The NEP appear, e.g., in stability analysis of time-delay systems, and as results of transformations of linear eigenvalue problems.

    This thesis mainly consists of 4 papers that treats the above mentioned computational problems, and presents both theory and methods. In paper A we consider a NEP stemming from the discretization of a partial differential equation describing wave propagation in a waveguide. Some NEP-methods require in each iteration to solve a linear system with a fixed matrix, but different right-hand sides, and with a fine discretization, this linear solve becomes the bottleneck. To overcome this we present a Sylvester-based preconditioner, exploiting the Sherman–Morrison–Woodbury formula.

    Paper B treats the generalized Sylvester equation and present two main results: First, a characterization that under certain assumptions motivates the existence of low-rank solutions. Second, a Krylov method applicable when the matrix coefficients are low-rank commuting, i.e., when the commutator is of low rank.

    In Paper C we study the generalized Lyapunov equation. Specifically, we extend the motivation for applying the alternating linear scheme (ALS) method, from the stable Lyapunov equation to the stable generalized Lyapunov equation. Moreover, we show connections to H2-optimal model reduction of associated bilinear systems, and show that ALS can be understood to construct a rank-1 model reduction subspace to such a bilinear system related to the residual. We also propose a residual-based generalized rational-Krylov-type subspace as a solver for the generalized Lyapunov equation.

    The fourth paper, Paper D, connects the NEP to the two-parameter eigenvalue problem. The latter is a generalization of the linear eigenvalue problem in the sense that there are two eigenvalue-eigenvector equations, both depending on two scalar variables. If we fix one of the variables, then we can use one of the equations, which is then a generalized eigenvalue problem, to solve for the other variable. In that sense, the solved-for variable can be understood as a family of functions of the first variable. Hence, it is a variable elimination technique where the second equation can be understood as a family of NEPs. Methods for NEPs can thus be adapted and exploited to solve the original problem. The idea can also be reversed, providing linearizations for certain NEPs.

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    Kappa Emil Ringh
  • 67.
    Georgiou, Tryphon T.
    et al.
    Univ Calif Irvine, Dept Mech & Aerosp Engn, Irvine, CA 92717 USA..
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Shanghai Jiao Tong Univ, Dept Automat, Shanghai, Peoples R China.;Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai, Peoples R China..
    On a Fejer-Riesz factorization of generalized trigonometric polynomials2021In: Communications in Information and Systems, ISSN 1526-7555, Vol. 21, no 3, p. 371-384Article in journal (Refereed)
    Abstract [en]

    Function theory on the unit disc proved key to a range of problems in statistics, probability theory, signal processing literature, and applications, and in this, a special place is occupied by trigonometric functions and the Fejer-Riesz theorem that non-negative trigonometric polynomials can be expressed as the modulus of a polynomial of the same degree evaluated on the unit circle. In the present note we consider a natural generalization of non-negative trigonometric polynomials that are matrix-valued with specified non-trivial poles (i.e., other than at the origin or at infinity). We are interested in the corresponding spectral factors and, specifically, we show that the factorization of trigonometric polynomials can be carried out in complete analogy with the Fej ' er-Riesz theorem. The affinity of the factorization with the Fej ' er-Riesz theorem and the contrast to classical spectral factorization lies in the fact that the spectral factors have degree smaller than what standard construction in factorization theory would suggest. We provide two juxtaposed proofs of this fundamental theorem, albeit for the case of strict positivity, one that relies on analytic interpolation theory and another that utilizes classical factorization theory based on the Yacubovich-Popov-Kalman (YPK) positive-real lemma.

  • 68.
    Ringh, Axel
    et al.
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Shanghai Jiao Tong Univ, Dept Automat, Shanghai, Peoples R China.;Shanghai Jiao Tong Univ, Sch Math, Shanghai, Peoples R China..
    On analytic interpolation with non-classical constraints for solving problems in robust control2021In: 2021 AMERICAN CONTROL CONFERENCE (ACC), IEEE , 2021, p. 2374-2381Conference paper (Refereed)
    Abstract [en]

    In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines the range of the interpolant, when evaluated on the imaginary axis, to a frequency-dependent set. By considering a sufficient condition for when this interpolation problem has a solution, we derive an approximate solution algorithm that can also be used for controller synthesis. The conservativeness of the method is reduced by introducing a shift, which can be tuned by the user. Finally, the theory is illustrated on a numerical example with a plant with uncertain gain, phase, and output delay.

  • 69.
    Haasler, Isabel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Chen, Y.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimal Steering of Ensembles with Origin-Destination Constraints2021In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 5, no 3, p. 881-886, article id 9131801Article in journal (Refereed)
    Abstract [en]

    We consider the optimal control problem of steering a collection of agents over a network. The group behavior of an ensemble is often modeled by a distribution, and thus the optimal control problem we study can be cast as a distribution steering problem. While most existing works for steering distributions require the agents in the ensemble to be indistinguishable, we consider the setting where agents have specified origin-destination constraints. This control problem also resembles a minimum cost network flow problem with a massive number of commodities. We propose a novel optimal transport based framework for this problem and derive an efficient algorithm for solving it. This framework extends multi-marginal optimal transport theory to settings with capacity and origin-destination constraints. The proposed method is illustrated on a numerical simulation for traffic planning.

  • 70.
    Yang, Bo
    et al.
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Peoples R China..
    Huang, Xuelin
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Peoples R China..
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Cheng, Weizheng
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Peoples R China..
    Pei, Zhiyong
    Wuhan Univ Technol, Cruise & Yacht Res Ctr, Green & Smart River Sea Going Ship, Wuhan 430063, Peoples R China..
    Li, Xu
    Wuhan Univ Technol, Sch Automat, Wuhan 430070, Peoples R China..
    Optimizing Robustness of Core-Periphery Structure in Complex Networks2021In: IEEE Transactions on Circuits and Systems - II - Express Briefs, ISSN 1549-7747, E-ISSN 1558-3791, Vol. 68, no 12, p. 3572-3576Article in journal (Refereed)
    Abstract [en]

    Complex networks can be considered as abstractions of complex systems existing in the real world. The potential functionality of networks is related to mesoscale structures in networks, among which the representative ones are community structure and core-periphery (CP) structure. Since many real-world networks will inevitably be attacked, it is of great significance to enhance robustness of networks. However, few of the existing studies about robustness have laid emphasis on robustness of CP structure. In this brief, we first propose a new index to measure the ability of CP structure to resist attacks or errors. Several efficient algorithms based on this index are then devised to maximize robustness of CP structure under reasonable constraint. Numerical results show that the robustness of the CP structure of several representative real-world networks is markedly enhanced. The structural changes in the optimized networks under study and their implication are also discussed.

  • 71. Tsay, C.
    et al.
    Kronqvist, Jan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Thebelt, A.
    Misener, R.
    Partition-Based Formulations for Mixed-Integer Optimization of Trained ReLU Neural Networks2021In: Advances in Neural Information Processing Systems, Neural information processing systems foundation , 2021, p. 3068-3080Conference paper (Refereed)
    Abstract [en]

    This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions via disjunctive programming. At one extreme, one partition per input recovers the convex hull of a node, i.e., the tightest possible formulation for each node. For fewer partitions, we develop smaller relaxations that approximate the convex hull, and show that they outperform existing formulations. Specifically, we propose strategies for partitioning variables based on theoretical motivations and validate these strategies using extensive computational experiments. Furthermore, the proposed scheme complements known algorithmic approaches, e.g., optimization-based bound tightening captures dependencies within a partition.

  • 72.
    Peng, Shen
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jiang, J.
    Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches2021In: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 80, no 1, p. 153-184Article in journal (Refereed)
    Abstract [en]

    In this paper, a class of stochastic mathematical programs with probabilistic complementarity constraints is considered. We first investigate convergence properties of sample average approximation (SAA) approach to the corresponding chance constrained relaxed complementarity problem. Our discussion can be not only applied to the specific model in this paper, but also viewed as a supplementary for the SAA approach to general joint chance constrained problems. Furthermore, considering the uncertainty of the underlying probability distribution, a distributionally robust counterpart with a moment ambiguity set is proposed. The numerically tractable reformulation is derived. Finally, we use a production planing model to report some preliminary numerical results. 

  • 73.
    Liu, Lizheng
    et al.
    School of Information Science and Teclmology, Fudan University, Shanghai, China.
    Wang, Deyu
    Wang, Yuning
    Lansner, Anders
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Hemani, Ahmed
    KTH, School of Electrical Engineering and Computer Science (EECS), Electrical Engineering, Electronics and Embedded systems, Electronic and embedded systems.
    Yang, Yu
    KTH, School of Electrical Engineering and Computer Science (EECS), Electrical Engineering, Electronics and Embedded systems, Electronic and embedded systems.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Zou, Zhuo
    Zheng, Lirong
    A FPGA-based Hardware Accelerator for Bayesian Confidence Propagation Neural Network2020In: 2020 IEEE Nordic Circuits and Systems Conference, NORCAS 2020 - Proceedings, Institute of Electrical and Electronics Engineers (IEEE) , 2020, article id 9265129Conference paper (Refereed)
    Abstract [en]

    The Bayesian Confidence Propagation Neural Network (BCPNN) has been applied in higher level of cognitive intelligence (e.g. working memory, associative memory). However, in the spike-based version of this learning rule the pre-, postsynaptic and coincident activity is traced in three low-passfiltering stages, the calculation processes of weight update are very computationally intensive. In this paper, a hardware architecture of the updating process for lazy update mode is proposed for updating 8 local synaptic state variables. The parallelism by decomposing the calculation steps of formulas based on the inherent data dependencies is optimized. The FPGA-based hardware accelerator of BCPNN is designed and implemented. The experimental results show the updating process on FPGA can be accomplished within 110 ns with a clock frequency of 200 MHz, the updating speed is greatly enhanced compared with the CPU test. The trade-off between performance, accuracy and resources on dedicated hardware is evaluated, and the impact of the module reuse on resource consumption and computing performance is evaluated.

  • 74.
    Liu, Lizheng
    et al.
    School of Information Science and Technology, Fudan University, Shanghai, China.
    Huan, Yuxiang
    School of Information Science and Technology, Fudan University, Shanghai, China.
    Zou, Zhou
    School of Information Science and Technology, Fudan University, Shanghai, China.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Zheng, Lirong
    School of Information Science and Technology, Fudan University, Shanghai, China.
    An Autonomous Error-Tolerant Architecture Featuring Self-reparation for Convolutional Neural Networks2020In: Proceeding of the IEEE Vehicular Technology Conference, Institute of Electrical and Electronics Engineers (IEEE) , 2020Conference paper (Refereed)
    Abstract [en]

    Convolutional neural networks are widely used in artificial intelligence and Internet of Things area. As the scale of convolutional neural network expands, more and more processing units are provided for it. The systems are easy prone to error, and any computing problems in any layer of the network will lead to wrong output results. Traditional multimode redundancy methods make the systems more complex, and increase power consumption. This paper proposes an autonomous error-tolerant architecture for convolutional neural networks. Taking the LeNet-5 as an example, the network layers of CNN are mapped on the AET architecture, an error-tolerant synapse is designed to discover the errors, an active evolution scheme is designed to handle unrecoverable errors and implement network reconfiguration. This design is implemented on FPGA, and the experimental results show that this architecture can realize effective error tolerance for convolutional neural network and has fast error recovery ability under the premise of ensuring the same recognition accuracy.

  • 75.
    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, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    An intrinsic approach to formation control of regular polyhedra for reduced attitudes2020In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 111, article id 108619Article in journal (Refereed)
    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.

  • 76.
    Ek, David
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Approaches to accelerate methods for solving systems of equations arising in nonlinear optimization2020Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Methods for solving nonlinear optimization problems typically involve solving systems of equations. This thesis concerns approaches for accelerating some of those methods. In our setting, accelerating involves finding a trade-off between the computational cost of an iteration and the quality of the computed search direction. We design approaches for which theoretical results in ideal settings are derived. We also investigate the practical performance of the approaches within and beyond the boundaries of the theoretical frameworks with numerical simulations.

    Paper A concerns methods for solving strictly convex unconstrained quadratic optimization problems. This is equivalent to solving systems of linear equations where the matrices are symmetric positive definite. The main focus is exact linesearch limited-memory quasi-Newton methods which generate search directions parallel to those of the method of preconditioned conjugate gradients. We give a class of limited-memory quasi-Newton methods. In addition, we provide a dynamic framework for the construction of these methods. The methods are meant to be particularly useful for solving sequences of related systems of linear equations. Such sequences typically arise as methods for solving systems of nonlinear equations converge.

    Paper B deals with solving systems of nonlinear equations that arise in interior-point methods for bound-constrained nonlinear programming. Application of Newton's method gives sequences of systems of linear equations. We propose partial and full approximate solutions to the Newton systems. The partial approximate solutions are computationally inexpensive, whereas each full approximate solution typically requires a reduced Newton system to be solved. In addition, we suggest two Newton-like approaches, which are based upon the proposed partial approximate solutions, for solving the systems of nonlinear equations.

    Paper C is focused on interior-point methods for quadratic programming. We propose a structured modified Newton approach to solve the systems of nonlinear equations that arise. The modified Jacobians are composed of a previous Jacobian, plus one low-rank update matrix per succeeding iteration. For a given rank restriction, we construct a low-rank update matrix such that the modified Jacobian becomes closest to the current Jacobian, in both 2-norm and Frobenious norm. The approach is structured in the sense that it preserves the nonzero pattern of the Jacobian.

    The approaches suggested in Paper B and Paper C are motivated by asymptotic results in ideal theoretical frameworks. In particular, it is shown that the approaches become increasingly accurate as primal-dual interior-point methods converge. A demonstration of the practical performance is given by numerical results. The results indicate the performance and limitations of the approaches suggested.

    We envisage that the approaches of Paper A, Paper B and Paper C can be useful in parallel, or in combination, with existing solvers in order to accelerate methods.

    Paper D is more pedagogical in nature. We give a derivation of the method of conjugate gradients in an optimization framework. The result itself is well known but the derivation has, to the best of our knowledge, not been presented before.

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  • 77.
    He, Xingkang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Xue, Wenchao
    LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China ; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
    Fang, Haitao
    LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China ; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Consistent Kalman filters for nonlinear uncertain systems over sensor networks2020In: Control Theory and Technology, ISSN 2095-6983, Vol. 18, no 4, p. 399-408Article in journal (Refereed)
    Abstract [en]

    In this paper, we study how to design filters for nonlinear uncertain systems over sensor networks. We introduce two Kalman-type nonlinear filters in centralized and distributed frameworks. Moreover, the tuning method for the parameters of the filters is established to ensure the consistency, i.e., the mean square error is upper bounded by a known parameter matrix at each time. We apply the consistent filters to the track-to-track association analysis of multi-targets with uncertain dynamics. A novel track-to-track association algorithm is proposed to identify whether two tracks are from the same target. It is proven that the resulting probability of mis-association is lower than the desired threshold. Numerical simulations on track-to-track association are given to show the effectiveness of the methods.

  • 78.
    Li, Yibei
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Harbin Inst Technol, Control & Simulat Ctr, Harbin 150001, Peoples R China..
    Yao, Yu
    Harbin Inst Technol, Control & Simulat Ctr, Harbin 150001, Peoples R China..
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Continuous-time inverse quadratic optimal control problem2020In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 117, article id 108977Article in journal (Refereed)
    Abstract [en]

    In this paper, the problem of finite horizon 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. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding standard linear quadratic (LQ) cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.

  • 79.
    Li, Yibei
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wang, Ximei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Credit scoring by incorporating dynamic networked information2020In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 286, no 3, p. 1103-1112Article in journal (Refereed)
    Abstract [en]

    In this paper, the credit scoring problem is studied by incorporating networked information, where the advantages of such incorporation are investigated theoretically in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide risk prediction for lenders assuming that published credit scores are estimated merely from structured financial data. Such prediction can then be used as a monitoring indicator for the risk management in lenders’ future decisions. Secondly, a recursive Bayes estimator is further proposed to improve the precision of credit scoring by incorporating the dynamic interaction topology of clients. It is shown theoretically that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cramér–Rao lower bound for clients within a certain range of scores. Finally, simulation results for a special case illustrate the feasibility and effectiveness of the proposed algorithms.

  • 80.
    Banert, Sebastian
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ringh, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Adler, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Elekta, Box 7593, S-10393 Stockholm, Sweden..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Data-driven nonsmooth optimization2020In: SIAM Journal on Optimization, ISSN 1052-6234, E-ISSN 1095-7189, Vol. 30, no 1, p. 102-131Article in journal (Refereed)
    Abstract [en]

    In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first parametrize a class of optimization methods using a generic iterative scheme involving only linear operations and applications of proximal operators. This scheme contains some modern primal-dual first-order algorithms like the Douglas-Rachford and hybrid gradient methods as special cases. Moreover, we show weak convergence of the iterates to an optimal point for a new method which also belongs to this class. Next, we interpret the generic scheme as a neural network and use unsupervised training to learn the best set of parameters for a specific class of objective functions while imposing a fixed number of iterations. In contrast to other approaches of "learning to optimize," we present an approach which learns parameters only in the set of convergent schemes. Finally, we illustrate the approach on optimization problems arising in tomographic reconstruction and image deconvolution, and train optimization algorithms for optimal performance given a fixed number of iterations.

  • 81.
    Xu, Jianqiang
    et al.
    East China Univ Sci & Technol, Shanghai 200237, Peoples R China..
    Hu, Zhujiao
    Fudan Univ, Sch Informat Sci & Technol, Shanghai 200433, Peoples R China..
    Zou, Zhuo
    Fudan Univ, Sch Informat Sci & Technol, Shanghai 200433, Peoples R China..
    Zou, Junzhong
    East China Univ Sci & Technol, Shanghai 200237, Peoples R China..
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Liu, Lizheng
    Fudan Univ, Sch Informat Sci & Technol, Shanghai 200433, Peoples R China.;Royal Inst Technol KTH, Optimizat & Syst Theory Dept Math, S-11428 Stockholm, Sweden..
    Zheng, Lirong
    Fudan Univ, Sch Informat Sci & Technol, Shanghai 200433, Peoples R China..
    Design of Smart Unstaffed Retail Shop Based on IoT and Artificial Intelligence2020In: IEEE Access, E-ISSN 2169-3536, Vol. 8, p. 147728-147737Article in journal (Refereed)
    Abstract [en]

    Unstaffed retail shops have emerged recently and been noticeably changing our shopping styles. In terms of these shops, the design of vending machine is critical to user shopping experience. The conventional design typically uses weighing sensors incapable of sensing what the customer is taking. In the present study, a smart unstaffed retail shop scheme is proposed based on artificial intelligence and the internet of things, as an attempt to enhance the user shopping experience remarkably. To analyze multiple target features of commodities, the SSD (300x300) algorithm is employed; the recognition accuracy is further enhanced by adding sub-prediction structure. Using the data set of 18, 000 images in different practical scenarios containing 20 different type of stock keeping units, the comparison experimental results reveal that the proposed SSD (300x300) model outperforms than the original SSD (300x300) in goods detection, the mean average precision of the developed method reaches 96.1% on the test dataset, revealing that the system can make up for the deficiency of conventional unmanned container. The practical test shows that the system can meet the requirements of new retail, which greatly increases the customer flow and transaction volume.

  • 82.
    Mattila, Robert
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    Centre de Mathématiques Appliquées de Polytechnique, Ecole Polytechnique, Paris, France.
    Moulines, E.
    Krishnamurthy, V.
    Wahlberg, Bo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Fast and consistent learning of hidden markov models by incorporating non-consecutive correlations2020In: 37th International Conference on Machine Learning, ICML 2020, International Machine Learning Society (IMLS) , 2020, p. 6741-6752Conference paper (Refereed)
    Abstract [en]

    Can the parameters of a hidden Markov model (HMM) be estimated from a single sweep through the observations - and additionally, without being trapped at a local optimum in the likelihood surface That is the premise of recent method of moments algorithms devised for HMMs. In these, correlations between consecutive pair-or tripletwise observations are empirically estimated and used to compute estimates of the HMM parameters. Albeit computationally very attractive, the main drawback is that by restricting to only loworder correlations in the data, information is being neglected which results in a loss of accuracy (compared to standard maximum likelihood schemes). In this paper, we propose extending these methods (both pair-and triplet-based) by also including non-consecutive correlations in a way which does not significantly increase the computational cost (which scales linearly with the number of additional lags included). We prove strong consistency of the new methods, and demonstrate an improved performance in numerical experiments on both synthetic and real-world financial timeseries datasets.

  • 83.
    Gao, Shigen
    et al.
    Beijing Jiaotong Univ, State Key Lab Rail Traff Control & Safety, Beijing 100044, Peoples R China..
    Wei, Jin
    Beijing Jiaotong Univ, State Key Lab Rail Traff Control & Safety, Beijing 100044, Peoples R China..
    Song, Haifeng
    Beijing Jiaotong Univ, Sch Elect & Informat Engn, Beijing 100044, Peoples R China..
    Zhang, Zixuan
    Beijing Jiaotong Univ, State Key Lab Rail Traff Control & Safety, Beijing 100044, Peoples R China..
    Dong, Hairong
    Beijing Jiaotong Univ, State Key Lab Rail Traff Control & Safety, Beijing 100044, Peoples R China..
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fuzzy adaptive automatic train operation control with protection constraints: A residual nonlinearity approximation-based approach2020In: Engineering applications of artificial intelligence, ISSN 0952-1976, E-ISSN 1873-6769, Vol. 96, article id 103986Article in journal (Refereed)
    Abstract [en]

    In this study, we present fuzzy adaptive control based on residual nonlinearity approximation in the presence of protection constraints for the target trajectory tracking problem observed in automatic train operation. Herein, protection constraints refer to a condition wherein the speed and position of a controlled train are not allowed to surpass the boundaries imposed by automatic train protection and moving authority. By defining proper coordinate transformation, the protection constraints are converted to an error-prescribed performance control problem that facilitates operational efficiency by reducing the margin with respect to target trajectories. Based on the prescribed performance control methodology, we present an improved scheme using fuzzy residual nonlinearity approximation and establish the uniformly ultimately boundedness (UUB) property. A novel feature therein is that the ultimate boundary of the proposed scheme is simultaneously characterized by the prescribed performance functions and control parameters, with rigorous and analytically mathematical expressions; while pioneering the prescribed performance control methodology, the ultimate boundary is characterized solely by the prescribed performance functions. To verify the effectiveness and advantages of the proposed scheme, the controllers are applied to the automatic train operation on the Beijing Yizhuang line, which contains 13 operational intervals. Finally, comparative and simulation results are presented to validate the proposed method.

  • 84.
    Fontan, Angela
    et al.
    Linköping Univ, Div Automat Control, Dept Elect Engn, SE-58183 Linköping, Sweden..
    Shi, Guodong
    Univ Sydney, Sch Aerosp Mech & Mechatron Engn, Australian Ctr Field Robot, Sydney, NSW 2008, Australia..
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Altafini, Claudio
    Linköping Univ, Div Automat Control, Dept Elect Engn, SE-58183 Linköping, Sweden..
    Interval Consensus for Multiagent Networks2020In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 65, no 5, p. 1855-1869Article in journal (Refereed)
    Abstract [en]

    The constrained consensus problem considered in this paper, denoted interval consensus, is characterized by the fact that each agent can impose a lower and upper bound on the achievable consensus value. Such constraints can be encoded in the consensus dynamics by saturating the values that an agent transmits to its neighboring nodes. We show in the paper that when the intersection of the intervals imposed by the agents is nonempty, the resulting constrained consensus problem must converge to a common value inside that intersection. In our algorithm, convergence happens in a fully distributed manner, and without need of sharing any information on the individual constraining intervals. When the intersection of the intervals is an empty set, the intrinsic nonlinearity of the network dynamics raises new challenges in understanding the node state evolution. Using Brouwer fixed-point theorem we prove that in that case there exists at least one equilibrium, and in fact the possible equilibria are locally stable if the constraints are satisfied or dissatisfied at the same time among all nodes. For graphs with sufficient sparsity it is further proven that there is a unique equilibrium that is globally attractive if the constraint intervals are pairwise disjoint.

  • 85.
    Li, Yibei
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH Royal Inst Technol, Stockholm, Sweden..
    Du, Juan
    South China Univ Technol, Guangzhou, Peoples R China..
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH Royal Inst Technol, Stockholm, Sweden..
    Intrinsic Formation Control Under Finite-Time Differential Game Framework2020In: Proceedings of the 39th chinese control conference / [ed] Fu, J Sun, J, IEEE , 2020, p. 4895-4900Conference paper (Refereed)
    Abstract [en]

    In this paper, the formation control problem of a multi-agent system is studied. The foraging behavior is modeled as a finite-horizon non-cooperative differential game under local information, and the existence and properties of Nash equilibria are studied. The formations are achieved in an intrinsic way in the sense that they are only attributed to the inter-agent interaction and geometric properties of the network, where the desired formations are not designated beforehand. Through the design of individual costs and network topology, regular polygons, antipodal formations and Platonic solids are achieved as Nash equilibria while inter-agent collision is avoided. While the focus is on the finite horizon case, it is also studied how the formation patterns would change as the length of the time interval tends to infinity. Finally, numerical simulations are provided in both two-dimensional and three-dimensional Euclidean space to demonstrate the effectiveness and feasibility of the proposed methods.

  • 86.
    Li, Yibei
    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.
    Intrinsic Formation of Regular Polyhedra: A Differential Game Approach2020In: Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc. , 2020, p. 4748-4753Conference paper (Refereed)
    Abstract [en]

    This paper addresses the intrinsic formation control problem of a multi-agent system. The foraging behavior of N agents is modeled as an infinite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The formations are achieved in an intrinsic way in the sense that they are only attributed to the inter-agent interaction and geometric properties of the network, where the desired formations are not designated beforehand. Through the design of individual costs and network topology, patterns of Platonic solids can be achieved as Nash equilibria while inter-agent collisions are avoided. Exponential convergence to the manifold of Platonic patterns is proved. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed methods. 

  • 87.
    Mattila, Robert
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Krishnamurthy, Vikram
    Wahlberg, Bo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Inverse Filtering for Hidden Markov Models With Applications to Counter-Adversarial Autonomous Systems2020In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 68, p. 4987-5002Article in journal (Refereed)
    Abstract [en]

    Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial autonomous systems, we consider the following inverse filtering problem: Given a sequence of posterior distributions from a Bayesian filter, what can be inferred about the transition kernel of the state, the observation likelihoods of the sensor and the measured observations? For finite-state Markov chains observed in noise (hidden Markov models), we show that a least-squares fit for estimating the parameters and observations amounts to a combinatorial optimization problem with non-convex objective. Instead, by exploiting the algebraic structure of the corresponding Bayesian filter, we propose an algorithm based on convex optimization for reconstructing the transition kernel, the observation likelihoods and the observations. We discuss and derive conditions for identifiability. As an application of our results, we demonstrate the design of a counter-adversarial autonomous system: By observing the actions of an autonomous enemy, we estimate the accuracy of its sensors and the observations it has received. The proposed algorithms are illustrated via several numerical examples.

  • 88.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Wahlberg, Bo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Learning sparse linear dynamic networks in a hyper-parameter free setting2020In: IFAC PAPERSONLINE, ELSEVIER , 2020, Vol. 53, no 2, p. 82-86Conference paper (Refereed)
    Abstract [en]

    We address the issue of estimating the topology and dynamics of sparse linear dynamic networks in a hyperparameter-free setting. We propose a method to estimate the network dynamics in a computationally efficient and parameter tuning-free iterative framework known as SPICE (Sparse Iterative Covariance Estimation). Our approach does not assume that the network is undirected and is applicable even with varying noise levels across the modules of the network. We also do not assume any explicit prior knowledge on the network dynamics. Numerical experiments with realistic dynamic networks illustrate the usefulness of our method. 

  • 89. Elvander, F.
    et al.
    Haasler, Isabel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jakobsson, A.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion2020In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 171, article id 107474Article in journal (Refereed)
    Abstract [en]

    During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, a common setup in many inverse problems in, e.g., remote sensing and imaging. By considering an entropy regularized approximation of the original transport problem, we propose an algorithm corresponding to a block-coordinate ascent of the dual problem, where Newton's algorithm is used to solve the sub-problems. In order to make this computationally tractable for large-scale settings, we utilize the tensor structure that arises in practical problems, allowing for computing projections of the multi-marginal transport plan using only matrix-vector operations of relatively small matrices. As illustrating examples, we apply the resulting method to tracking and barycenter problems in spatial spectral estimation. In particular, we show that the optimal mass transport framework allows for fusing information from different time steps, as well as from different sensor arrays, also when the sensor arrays are not jointly calibrated. Furthermore, we show that by incorporating knowledge of underlying dynamics in tracking scenarios, one may arrive at accurate spectral estimates, as well as faithful reconstructions of spectra corresponding to unobserved time points.

  • 90.
    Pereira, Goncalo Collares
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Centres, Integrated Transport Research Lab, ITRL. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Lima, P. F.
    Wahlberg, Bo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Pettersson, H.
    Mårtensson, Jonas
    KTH, School of Engineering Sciences (SCI), Applied Physics, Biomedical and X-ray Physics. KTH, School of Industrial Engineering and Management (ITM), Centres, Integrated Transport Research Lab, ITRL. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Nonlinear Curvature Modeling for MPC of Autonomous Vehicles2020In: 2020 IEEE 23rd International Conference on Intelligent Transportation Systems, ITSC 2020, Institute of Electrical and Electronics Engineers (IEEE) , 2020Conference paper (Refereed)
    Abstract [en]

    This paper investigates how to compensate for curvature response mismatch in lateral Model Predictive Control (MPC) of an autonomous vehicle. The standard kinematic bicycle model does not describe accurately the vehicle yaw-rate dynamics, leading to inaccurate motion prediction when used in MPC. Therefore, the standard model is extended with a nonlinear function that maps the curvature response of the vehicle to a given request. Experimental data shows that a two Gaussian functions approximation gives an accurate description of this mapping. Both simulation and experimental results show that the corresponding modified model significantly improves the control performance when using Reference Aware MPC for autonomous driving of a Scania heavy-duty construction truck.

  • 91.
    Böck, Michelle
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Labs AB, S-11134 Stockholm, Sweden.;Dana Farber Canc Inst, Brigham & Womens Hosp, Dept Radiat Oncol, Boston, MA 02115 USA.;Harvard Med Sch, Boston, MA 02115 USA..
    On adaptation cost and tractability in robust adaptive radiation therapy optimization2020In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 47, no 7, p. 2791-2804Article in journal (Refereed)
    Abstract [en]

    Purpose In this paper, a framework for online robust adaptive radiation therapy (ART) is discussed and evaluated. The purpose of the presented approach to ART is to: (a) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (b) address adaptation cost, and Methods A novel framework for online robust ART using the concept of Bayesian inference and scenario reduction is introduced and evaluated in a series of simulated cases 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. Throughout the course of treatment, the simulated interfractional variations are evaluated in terms of their likelihood with respect to the a priori hypothesis of their distribution and violation of user-specified tolerance limits by the accumulated dose. If an adaptation is considered, the a posteriori distribution is computed from the actual variations using Bayesian inference. Then, the adapted plan is optimized to better suit the actual interfractional variations of the individual case. This adapted plan is used until the next adaptation is triggered. To address adaptation cost, the proposed framework provides an option for increased adaptation frequency. Computational tractability in robust planning and ART is addressed by an approximation algorithm to reduce the size of the optimization problem. Results According to the simulations, the proposed framework may improve target coverage compared to the corresponding nonadaptive robust approach. In particular, Bayesian inference may be useful to individualize plans to the actual interfractional variations. Concerning adaptation cost, the results indicate that mathematical methods like Bayesian inference may have a greater impact on improving individual treatment quality than increased adaptation frequency. In addition, the simulations suggest that the concept of scenario reduction may be useful to address computational tractability in ART and robust planning in general. Conclusions The simulations indicate that the adapted plans may improve target coverage and OAR protection at manageable adaptation and computational cost within the novel framework. In particular, adaptive strategies using Bayesian inference appear to perform best among all strategies. This proof-of-concept study provides insights into the mathematical aspects of robustness, tractability, and ART, which are a useful guide for further development of frameworks for online robust ART.

  • 92.
    Forsgren, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wang, Fei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On the existence of a short pivoting sequence for a linear program2020In: Operations Research Letters, ISSN 0167-6377, E-ISSN 1872-7468, Vol. 48, no 6, p. 697-702Article in journal (Refereed)
    Abstract [en]

    We show that given a feasible primal–dual pair of linear programs in canonical form, there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, leading from the origin to the optimum. The sequence of pivots give a sequence of square and nonsingular submatrices of the constraint matrix. Solving two linear equations involving such a submatrix give primal–dual optimal solutions to the corresponding linear program in canonical form.

  • 93.
    Mele, Giampaolo
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Ringh, Emil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Ek, David
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Izzo, Federico
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Upadhyaya, Parikshit
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Jarlebring, Elias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Preconditioning for linear systems2020Book (Other academic)
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  • 94. Ghosh, B. K.
    et al.
    Hu, J.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Special issue on emerging challenges in multi-agent sensing, control and optimization2020In: Control Theory and Technology, ISSN 2095-6983, Vol. 18, no 4, p. 337-338Article in journal (Refereed)
  • 95.
    Böck, Michelle
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Brigham & Womens Hosp, 75 Francis St, Boston, MA 02115 USA.;Dana Farber Canc Inst, Boston, MA 02115 USA.;Harvard Med Sch, Boston, MA 02115 USA.;RaySearch Labs AB, Stockholm, Sweden..
    Towards a Mathematical Framework to Address Uncertainty, Adaptation Cost and Tractability in Robust Adaptive Radiation Therapy2020In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 47, no 6, p. E666-E666Article in journal (Other academic)
  • 96.
    Özkahraman, Özer
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Robotics, Perception and Learning, RPL.
    Ögren, Petter
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Robotics, Perception and Learning, RPL.
    Underwater Caging and Capture for Autonomous Underwater Vehicles2020In: Global Oceans 2020: Singapore - U.S. Gulf Coast, Institute of Electrical and Electronics Engineers (IEEE) , 2020Conference paper (Refereed)
    Abstract [en]

    In this paper, we consider the problem of caging and eventual capture of an underwater entity using multiple Autonomous Underwater Vehicles (AUVs) in a 3D water volume We solve this problem both with and without taking bathymetry into account. Our proposed algorithm for range-limited sensing in 3D environments captures a finite-speed entity based on sparse and irregular observations. After an isolated initial sighting of the entity, the uncertainty of its whereabouts grows while deployment of the AUV system is underway. To contain the entity, an initial cage, or barrier of sensing footprints, is created around the initial sighting, using islands and other terrain as part of the cage if available. After the initial cage is established, the system waits for a second sighting, and the possible opportunity to create a smaller, shrinkable cage. This process continues until at some point it is possible to create this smaller cage, resulting in capture, meaning the entity is sensed directly and continuously. We present a set of algorithms for addressing the scenario above, and illustrate their performance on a set of examples. The proposed algorithm is a combination of solutions to the min-cut problem, the set cover problem, the linear bottleneck assignment problem and the Thomson problem.

    Download full text (pdf)
    fulltext
  • 97.
    Enqvist, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Svensson, Göran
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A Marginal Allocation Approach to Resource Management for a System of Multiclass Multiserver Queues Using Abandonment and CVaR QoS Measures2019In: 7th International Conference on Operations Research and Enterprise Systems, ICORES 2018, Springer Verlag , 2019, p. 119-133Conference paper (Refereed)
    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.

  • 98.
    Enqvist, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Svensson, Göran
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A state dependent chat system model2019In: ICORES 2019 - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems, SciTePress , 2019, p. 121-132Conference paper (Refereed)
    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. 

  • 99.
    Wang, Ximei
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Credit rating analysis based on the network of trading information2019In: The journal of network theory in finance, ISSN 2055-7795, Vol. 5, no 1, p. 47-65Article in journal (Refereed)
    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.

  • 100. Hu, C.
    et al.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hong, Y.
    Distributed adaptive Kalman filter based on variational Bayesian technique2019In: Control Theory and Technology, ISSN 2095-6983, Vol. 17, no 1, p. 37-47Article in journal (Refereed)
    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.

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