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  • 51. Hashimoto, K.
    et al.
    Adachi, S.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Self-Triggered Model Predictive Control for Nonlinear Input-Affine Dynamical Systems via Adaptive Control Samples Selection2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 1, p. 177-189, article id 7423697Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose a self-Triggered formulation of model predictive control for continuous-Time nonlinear input-Affine networked control systems. Our control method specifies not only when to execute control tasks but also provides a way to discretize the optimal control trajectory into several control samples, so that the reduction of communication load will be obtained. Stability analysis under the sample-And-hold implementation is also given, which guarantees that the state converges to a terminal region where the system can be stabilized by a local state feedback controller. Some simulation examples validate our proposed framework.

  • 52.
    Hashimoto, Kazumune
    et al.
    Keio Univ, Dept Appl Phys & Physicoinformat, Tokyo 1088345, Japan..
    Adachi, Shuichi
    Keio Univ, Dept Appl Phys & Physicoinformat, Tokyo 1088345, Japan..
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Aperiodic Sampled-Data Control via Explicit Transmission Mapping: A Set-Invariance Approach2018In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 10, p. 3523-3530Article in journal (Refereed)
    Abstract [en]

    Event-triggered and self-triggered control have been proposed in recent years as promising control strategies to reduce communication resources in networked control systems (NCSs). Based on the notion of set-invariance theory, this note presents new self-triggered control strategies for linear discrete-time systems subject to input and state constraints. The proposed schemes not only achieve communication reduction for NCSs, but also ensure both asymptotic stability of the origin and constraint satisfactions. A numerical simulation example validates the effectiveness of the proposed approaches.

  • 53. Hendrickx, Julien M.
    et al.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jungers, Raphael M.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sou, Kin Cheong
    Efficient Computations of a Security Index for False Data Attacks in Power Networks2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 12, p. 3194-3208Article in journal (Refereed)
    Abstract [en]

    The resilience of Supervisory Control and Data Acquisition (SCADA) systems for electric power networks for certain cyber-attacks is considered. We analyze the vulnerability of the measurement system to false data attack on communicated measurements. The vulnerability analysis problem is shown to be NP-hard, meaning that unless P = NP there is no polynomial time algorithm to analyze the vulnerability of the system. Nevertheless, we identify situations, such as the full measurement case, where the analysis problem can be solved efficiently. In such cases, we show indeed that the problem can be cast as a generalization of the minimum cut problem involving nodes with possibly nonzero costs. We further show that it can be reformulated as a standard minimum cut problem (without node costs) on a modified graph of proportional size. An important consequence of this result is that our approach provides the first exact efficient algorithm for the vulnerability analysis problem under the full measurement assumption. Furthermore, our approach also provides an efficient heuristic algorithm for the general NP-hard problem. Our results are illustrated by numerical studies on benchmark systems including the IEEE 118-bus system.

  • 54. Hendrickx, Julien M.
    et al.
    Shi, Guodong
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Finite-Time Consensus Using Stochastic Matrices With Positive Diagonals2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 4, p. 1070-1073, article id 6887337Article in journal (Refereed)
    Abstract [en]

    We discuss the possibility of reaching consensus in finite time using only linear iterations, with the additional restrictions that the update matrices must be stochastic with positive diagonals and consistent with a given graph structure. We show that finite-time average consensus can always be achieved for connected undirected graphs. For directed graphs, we show some necessary conditions for finite-time consensus, including strong connectivity and the presence of a simple cycle of even length.

  • 55.
    Hjalmarsson, Håkan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mårtensson, Jonas
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Geometric Approach to Variance Analysis in System Identification2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 5, p. 983-997Article in journal (Refereed)
    Abstract [en]

    This paper addresses the problem of quantifying the model error ("variance-error") in estimates of dynamic systems. It is shown that, under very general conditions, the asymptotic ( in data length) covariance of an estimated system property ( represented by a smooth function of estimated system parameters) can be interpreted in terms of an orthogonal projection of a certain function, associated with the property of interest, onto a subspace determined by the model structure and experimental conditions. The presented geometric approach simplifies structural analysis of the model variance and this is illustrated by analyzing the influence of inputs and sensors on the model accuracy.

  • 56.
    Hu, Xiaoming
    KTH, Superseded Departments, Mathematics.
    Control of mobile platforms using a virtual vehicle approach2001In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 46, no 11, p. 1777-1782Article in journal (Refereed)
    Abstract [en]

    Two model independent solutions to the problem of controlling wheel-based mobile platforms are proposed. These two algorithms are based on a so called virtual vehicle approach, where the motion of the reference point on the desired trajectory is governed by a differential equation containing error feedback. This, combined with the fact that the proven stable control algorithms are basically proportional regulators with arbitrary positive gains, make the solutions robust with respect to errors and disturbances, as demonstrated by the experimental results.

  • 57.
    Hu, Xiaoming
    KTH, Superseded Departments, Mathematics.
    Observers for systems with implicit output2000In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 45, no 1, p. 168-173Article in journal (Refereed)
    Abstract [en]

    In this correspondence, we prove the convergence of Luenberger-type observers for systems with implicitly defined outputs.

  • 58.
    Huang, Lirong
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Multi-Time-Scale Generalization of Recursive Identification Algorithm for ARMAX Systems2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 8, p. 2242-2247Article in journal (Refereed)
    Abstract [en]

    Recently, Chen (2010) presented a new approach to recursive identification for ARMAX systems, which is a three-stage recursive scheme and assumes independent and identically distributed input signals. Here, we observe that, unless the time scale of the algorithm at one stage is reasonably faster than those at the previous stages, convergence to the true value may not take place. To remedy this issue, this note proposes a multi-time-scale modification of the algorithm in [ 5] such that convergence is achieved. In addition, the new scheme handles a wider class of input signals so that the input can be designed for some purpose. The advantage of the multi-time scale algorithm is verified with numerical examples.

  • 59.
    Huang, Lirong
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Mao, Xuerong
    Stability of Singular Stochastic Systems With Markovian Switching2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 2, p. 424-429Article in journal (Refereed)
    Abstract [en]

    In recent years, singular hybrid systems have received considerable attention. However, few results are concerned with stability of singular hybrid stochastic systems. Based on a stability result for singular hybrid systems, this note studies mean-square stability of singular hybrid stochastic systems. It is found that the diffusions and the Markov chain may play important roles in system analysis in mean-square sense. As a special case, a criterion for mean-square stability of hybrid stochastic systems is developed by the frequency domain approach.

  • 60. Ishizaki, Takayuki
    et al.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Kashima, Kenji
    Imura, Jun-ichi
    Aihara, Kazuyuki
    Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 4, p. 1023-1037Article in journal (Refereed)
    Abstract [en]

    We propose a dissipativity-preserving structured model reduction method for distributed control systems. As a fundamental tool to develop structured model reduction, we first establish dissipativity-preserving model reduction for general linear systems on the basis of a singular perturbation approximation. To this end, by deriving a tractable expression of singular perturbation models, we characterize dissipativity preservation in terms of a projection-like transformation of storage functions, and we show that the resultant approximation error is relevant to the sum of neglected eigenvalues of an index matrix. Next, utilizing this dissipativity-preserving model reduction, we develop a structured controller reduction method for distributed control systems. The major significance of this method is to preserve the spatial distribution of dissipative controllers and to provide an a priori bound for the performance degradation of closed-loop systems in terms of the H-2-norm. The efficiency of the proposed method is verified through a numerical example of vibration suppression control for interconnected second-order systems.

  • 61. Jacobsson, Krister
    et al.
    Andrew, Lachlan L. H.
    Tang, Ao
    Low, Steven H.
    California Institute of Technology.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    An Improved Link Model for Window Flow Control and Its Application to FAST TCP2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 3, p. 551-564Article in journal (Refereed)
    Abstract [en]

    This paper presents a link model which captures the queue dynamics In response to a change in a transmission control protocol (TCP) source's congestion window. By considering both self-clocking and the link integrator effect, the model generalizes existing models and is shown to be more accurate by both open loop and closed loop packet level simulations. It reduces to the known static link model when flows' round trip delays are identical, and approximates the standard integrator link model when there is significant cross traffic. We apply this model to the stability analysis of fast active queue management scalable TCP (FAST TCP) Including its filter dynamics. Under this model, the FAST control law is linearly stable for a single bottleneck link with an arbitrary distribution of round trip delays. This result resolves the notable discrepancy between empirical observations and previous theoretical predictions. The analysis highlights the critical role of self-clocking in TCP stability, and the proof technique is new and less conservative than existing ones.

  • 62. Jakobsson, Martin
    et al.
    Magnusson, Sindri
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Fischione, Carlo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Weeraddana, Pradeep Chathuranga
    Sri Lankan Institute of Information Technology.
    Extensions of Fast-Lipschitz Optimization2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 4, p. 861-876Article in journal (Refereed)
    Abstract [en]

    The need of fast distributed solvers for optimizationproblems in networked systems has motivated the recent developmentof the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying conditions,such as monotonicity of the objective function and contractivityof the constraints, have a unique optimal solution obtained via fast distributed algorithms that compute the fixed point of the constraints. This paper extends the set of problems for which the Fast-Lipschitz framework applies. Existing assumptions on the problem form are relaxed and new and generalized qualifying conditions are established by novel results based on Lagrangianduality. It is shown for which cases of more constraints thandecision variables, and less constraints than decision variables Fast-Lipschitz optimization applies. New results are obtained by imposing non strict monotonicity of the objective functions. The extended Fast-Lipschitz framework is illustrated by a number ofexamples, including network optimization and optimal control problems.

  • 63.
    Jansson, Henrik
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Input design via LMIs admitting frequency-wise model specifications in confidence regions2005In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 50, no 10, p. 1534-1549Article in journal (Refereed)
    Abstract [en]

    A framework for reformulating input design problems in prediction error identification as convex optimization problems is presented. For linear time-invariant single input/single output systems, this framework unifies and extends existing results on open-loop input design that are based on the finite dimensional asymptotic covariance matrix of the parameter estimates. Basic methods for parametrizing the input spectrum are provided and conditions on these parametrizations that guarantee that all possible covariance matrices for the asymptotic distribution of the parameter estimates can be generated are provided. A wide range of model quality constraints can be handled. In particular, different frequency-by-frequency constraints can be used. This opens up new applications of input design in areas such as robust control. Furthermore, quality specifications can be imposed on all models in a confidence region. Thus, allowing for statements such as with at 99% probability the model quality specifications will be satisfied.

  • 64.
    Jarlebring, Elias
    et al.
    Katholieke Univ Leuven, B-3001 Louvain, Belgium .
    Vanbiervliet, J
    Katholieke Univ Leuven, B-3001 Louvain, Belgium .
    Michiels, Wim
    Katholieke Univ Leuven, B-3001 Louvain, Belgium .
    Characterizing and Computing the H(2) Norm of Time-Delay Systems by Solving the Delay Lyapunov Equation2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 4, p. 814-825Article in journal (Refereed)
    Abstract [en]

    It is widely known that the solutions of Lyapunov equations can be used to compute the norm of linear time-invariant (LTI) dynamical systems. In this paper, we show how this theory extends to dynamical systems with delays. The first result is that the norm can be computed from the solution of a generalization of the Lyapunov equation, which is known as the delay Lyapunov equation. From the relation with the delay Lyapunov equation we can prove an explicit formula for the norm if the system has commensurate delays, here meaning that the delays are all integer multiples of a basic delay. The formula is explicit and contains only elementary linear algebra operations applied to matrices of finite dimension. The delay Lyapunov equations are matrix boundary value problems. We show how to apply a spectral discretization scheme to these equations for the general, not necessarily commensurate, case. The convergence of spectral methods typically depends on the smoothness of the solution. To this end we describe the smoothness of the solution to the delay Lyapunov equations, for the commensurate as well as for the non-commensurate case. The smoothness properties allow us to completely predict the convergence order of the spectral method

  • 65.
    Jin, Ming
    et al.
    Univ Calif Berkeley, Dept Ind Engn & Operat Res, Berkeley, CA 94720 USA..
    Lavaei, Javad
    Univ Calif Berkeley, Dept Ind Engn & Operat Res, Berkeley, CA 94720 USA..
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Power Grid AC-Based State Estimation: Vulnerability Analysis Against Cyber Attacks2019In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 64, no 5, p. 1784-1799Article in journal (Refereed)
    Abstract [en]

    To ensure grid efficiency and reliability, power system operators continuously monitor the operational characteristics of the grid through a critical process called state estimation (SE), which performs the task by filtering and fusing various measurements collected from grid sensors. This study analyzes the vulnerability of the key operation module, namely ac-based SE, against potential cyber attacks on data integrity, also known as false data injection attack (FDIA). A general form of FDIA can be formulated as an optimization problem, whose objective is to find a stealthy and sparse data injection vector on the sensor measurements with the aim of making the state estimate spurious and misleading. Due to the nonlinear ac measurement model and the cardinality constraint, the problem includes both continuous and discrete nonlinearities. To solve the FDIA problem efficiently, we propose a novel convexification framework based on semidefinite programming (SDP). By analyzing a globally optimal SDP solution, we delineate the "attackable region" for any given set of measurement types and grid topology, where the spurious state can be falsified by FDIA. Furthermore, we prove that the attack is stealthy and sparse, and derive performance bounds. Simulation results on various IEEE test cases indicate the efficacy of the proposed convexification approach. From the grid protection point of view, the results of this study can be used to design a security metric for the current practice against cyber attacks, redesign the bad data detection scheme, and inform proposals of grid hardening. From a theoretical point of view, the proposed framework can be used for other nonconvex problems in power systems and beyond.

  • 66.
    Johansson, Karl H.
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Barabanov, A. E.
    Astrom, K. J.
    Limit cycles with chattering in relay feedback systems2002In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 47, no 9, p. 1414-1423Article in journal (Refereed)
  • 67.
    Johansson, Karl H.
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pappas, George J.
    Tabuada, Paulo
    Tomlin, Claire J.
    Special Issue on Control of Cyber-Physical Systems2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 12, p. 3120-3121Article in journal (Other academic)
  • 68. Johansson, Karl Henrik
    et al.
    Rantzer, A.
    Decentralized control of sequentially minimum phase systems1999In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 44, no 10, p. 1909-1913Article in journal (Refereed)
    Abstract [en]

    Fundamental limitations in decentralized control of systems with multivariable zeros are considered. It is shown that arbitrary bandwidth can be obtained with a stable block-diagonal controller, if certain subsystems of the open-loop system fail to have zeros in the right half-plane and a high-frequency condition holds. Implications on control structure design and sequential loop-closuring methods are discussed.

  • 69.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    A cutting plane algorithm for robustness analysis of periodically time-varying systems2001In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 46, no 4, p. 579-592Article in journal (Refereed)
    Abstract [en]

    An algorithm for robustness analysis of periodic systems is derived. The system under consideration consists of a linear periodically time-varying plant in feedback interconnection with a structured uncertainty, Conditions for robust stability and robust performance can be formulated in terms of periodic integral quadratic constraints (IQCs), in this way, the robustness analysis becomes a problem of optimizing the parameters of the IQC. A cutting plane algorithm is suggested for solving this infinite-dimensional optimization problem.

  • 70.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    Robustness of periodic trajectories2002In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 47, no 11, p. 1842-1856Article in journal (Refereed)
    Abstract [en]

    A robustness problem for periodic trajectories is considered in this paper. A nonautonomous system with a periodic solution is given. The problem is to decide whether a stable periodic solution remains in a neighborhood of the nominal periodic solution when, the dynamics of the system is perturbed. The case with a structured dynamic perturbation is considered. This makes the problem a nontrivial generalization of a classical problem in the theory of dynamical systems. A solution to the robustness problem will be obtained by using a variational system obtained by linearizing the system dynamics along a trajectory, which is uncertain but within the prespecified neighborhood of the nominal trajectory. This gives rise to robustness conditions that can be solved using integral quadratic constraints for linear time periodic systems.

  • 71. Jönsson, Ulf T.
    The Zames-Falb IQC for systems with integrators2000In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 45, no 3, p. 560-565Article in journal (Refereed)
    Abstract [en]

    A feedback interconnection of a neutrally stable, linear time-invariant system and a nonlinearity with 0 less than or equal to x phi(x) less than or equal to kx(2) is called critical because the worst case linearization is at best neutrally stable. This characteristic makes the stability analysis of such systems particularly hard. It will be shown that an integrator and a sector bounded nonlinearity can be encapsulated in a bounded operator that satisfies several useful integral quadratic constraints, which gives powerful tools for stability analysis of a general class of critically stable systems.

  • 72.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, C. -Y
    Consensus of heterogeneous LTI agents2012In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, no 8, p. 2133-2139Article in journal (Refereed)
    Abstract [en]

    A robust stability criterion is derived for a class of higher order consensus algorithms. In distinction to the standard consensus problem where the dynamics of all individual agents are the same and of low dimension, the criterion for reaching consensus now depends on the full spectrum of the communication graph and not only the largest nonzero eigenvalue. The new consensus criterion is posed as a Nyquist-like criterion that provides a clear separation between the individual dynamics and the spectrum of the graph. Our results are illustrated on a formation control problem for a target encircling task.

  • 73.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung-Yao
    A Scalable Robust Stability Criterion for Systems With Heterogeneous LTI Components2010In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 10, p. 2219-2234Article in journal (Refereed)
    Abstract [en]

    A scalable robust stability criterion for interconnected systems with heterogeneous linear time-invariant components is presented in this paper. The criterion involves only the properties of individual components and the spectrum of the interconnection matrix, which can be verified with relatively low computational effort, and more importantly maintains scalability of the analysis. Our main result shows that if the components are single-input-single-output (SISO), then the criterion has an appealing graphical interpretation which resembles the classical Nyquist criterion.

  • 74.
    Karlsson, Johan
    et al.
    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, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Georgiou, Tryphon T.
    Department of Electrical Engineering, University of Minnesota.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    The Inverse Problem of Analytic Interpolation With Degree Constraint and Weight Selection for Control Synthesis2010In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 2, p. 405-418Article in journal (Refereed)
    Abstract [en]

    The minimizers of certain weighted entropy functionals are the solutions to an analytic interpolation problem with a degree constraint, and all solutions to this interpolation problem arise in this way by a suitable choice of weights. Selecting appropriate weights is pertinent to feedback control synthesis, where interpolants represent closed-loop transfer functions. In this paper we consider the correspondence between weights and interpolants in order to systematize feedback control synthesis with a constraint on the degree. There are two basic issues that we address: we first characterize admissible shapes of minimizers by studying the corresponding inverse problem, and then we develop effective ways of shaping minimizers via suitable choices of weights. This leads to a new procedure for feedback control synthesis.

  • 75.
    Karlsson, Johan
    et al.
    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, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    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, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Degree-Constrained Analytic Interpolation With Interpolation Points Close to the Boundary2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 6, p. 1412-1418Article in journal (Refereed)
    Abstract [en]

    In the recent article [4], a theory for complexity-constrained interpolation of contractive functions is developed. In particular, it is shown that any such interpolant may be obtained as the unique minimizer of a (convex) weighted entropy gain. In this technical note we study this optimization problem in detail and describe how the minimizer depends on weight selection and on interpolation conditions. We first show that, if, for a sequence of interpolants, the values of the entropy gain of the interpolants converge to the optimum, then the interpolants converge in H-2, but not in H-infinity This result is then used to describe the asymptotic behavior of the interpolant as an interpolation point approaches the boundary of the domain of analyticity. For loop shaping to specifications in control design, it might at first seem natural to place strategically additional interpolation points close to the boundary. However, our results indicate that such a strategy will have little effect on the shape. Another consequence of our results relates to model reduction based on minimum-entropy principles, where one should avoid placing interpolation points too close to the boundary.

  • 76.
    Karlsson, Johan
    et al.
    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, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    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, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Stability-preserving rational approximation subject to interpolation constraints2008In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 53, no 7, p. 1724-1730Article in journal (Refereed)
    Abstract [en]

    A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational analytic interpolants with an a priori bound, has been developed in recent years. In this paper, we consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to weighted H-2 minimization, where the interpolants are parameterized by the weights. The inverse problem of determining the weight given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded analytic interpolants.

  • 77.
    Khina, Anatoly
    et al.
    CALTECH, Dept Elect Engn, Pasadena, CA 91125 USA.;Tel Aviv Univ, Dept Elect Engn Syst, IL-6997801 Tel Aviv, Israel..
    Gårding, Elias Riedel
    KTH, School of Engineering Sciences (SCI). Univ Cambridge, Dept Appl Math & Theoret Phys, Ctr Math Sci, Cambridge CB3 0WA, England..
    Pettersson, Gustav M.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    Kostina, Victoria
    CALTECH, Dept Elect Engn, Pasadena, CA 91125 USA..
    Hassibi, Babak
    CALTECH, Dept Elect Engn, Pasadena, CA 91125 USA..
    Control Over Gaussian Channels With and Without Source-Channel Separation2019In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 64, no 9, p. 3690-3705Article in journal (Refereed)
    Abstract [en]

    We consider the problem of controlling an unstable linear plant with Gaussian disturbances over an additive white Gaussian noise channel with an average transmit power constraint, where the signaling rate of communication may be different from the sampling rate of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and that is often lower than the signaling rate of the communication channel. This rate mismatch offers the opportunity of improving the system performance by using coding over multiple channel uses to convey a single control action. In a traditional, separation-based approach to source and channel coding, the analog message is first quantized down to a few bits and then mapped to a channel codeword whose length is commensurate with the number of channel uses per sampled message. Applying the separation-based approach to control meets its challenges: first, the quantizer needs to be capable of zooming in and out to be able to track unbounded system disturbances, and second, the channel code must be capable of improving its estimates of the past transmissions exponentially with time, a characteristic known as anytime reliability. We implement a separated scheme by leveraging recently developed techniques for control over quantized-feedback channels and for efficient decoding of anytime-reliable codes. We further propose an alternative, namely, to perform analog joint source-channel coding, by this avoiding the digital domain altogether. For the case where the communication signaling rate is twice the sampling rate, we employ analog linear repetition as well as Shannon-Kotel'nikov maps to show a significant improvement in stability margins and linear-quadratic costs over separation-based schemes. We conclude that such analog coding performs better than separation, and can stabilize all moments as well as guarantee almost-sure stability.

  • 78. Leong, Alex S.
    et al.
    Quevedo, Daniel E.
    Ahlen, Anders
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Network Topology Reconfiguration for Remote State Estimation2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 12, p. 3842-3856Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate network topology reconfiguration in wireless sensor networks for remote state estimation, where sensor observations are transmitted, possibly via intermediate sensors, to a central gateway/estimator. The time-varying wireless network environment is modelled by the notion of a network state process, which is a randomly time-varying semi-Markov chain and determines the packet reception probabilities of links at different times. For each network state, different network configurations can be used, which govern the network topology and routing of packets. The problem addressed is to determine the optimal network configuration to use in each network state, in order to minimize an expected error covariance measure. Computation of the expected error covariance cost function has a complexity of O(2(M Delta max)), where M is the number of sensors and Delta max is the maximum time between transitions of the semi-Markov chain. A sub-optimal method which minimizes the upper bound of the expected error covariance, that can be computed with a reduced complexity of O(2(M)), is proposed, which in many cases gives identical results to the optimal method. Conditions for estimator stability under both the optimal and suboptimal reconfiguration methods are derived using stochastic Lyapunov functions. Numerical results and comparisons with other low complexity approaches demonstrate the performance benefits of our approach.

  • 79.
    Lindquist, Anders
    KTH, Superseded Departments, Mathematics.
    Generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint2001In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 46, no 6, p. 822-839Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a generalized entropy criterion for solving the rational Nevanlinna-Pick problem for n + 1 interpolating conditions and the degree of interpolants bounded by n, The primal problem of maximizing this entropy gain has a very well-behaved dual problem. This dual is a convex optimization problem in a finite-dimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most n, The criterion requires a selection of a monic Schur polynomial of degree n, It follows that this class of monic polynomials completely parameterizes all such rational interpolants, and it therefore provides a set of design parameters for specifying such interpolants. The algorithm is implemented in state-space form and applied to several illustrative problems in systems and control, namely sensitivity minimization, maximal power transfer and spectral estimation.

  • 80.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Matrix-valued Nevanlinna-pick interpolation with complexity constraint: An optimization approach2003In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 48, no 12, p. 2172-2190Article in journal (Refereed)
    Abstract [en]

    Over the last several years, a new theory of Nevanlinna-Pick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrix-valued, case, also allowing for multiple interpolation points. We parameterize a class of interpolants consisting of "most interpotants" of no higher degree than the central solution in terms of spectral zeros. This is a complete parameterization, and for each choice of interpolant we provide a convex optimization problem for determining it. This is derived in the context of duality theory of mathematical programming. To solve the convex optimization problem, we employ a homotopy continuation technique previously developed for the scalar case. These results can be applied to many classes of engineering problems,and, to illustrate this, we provide some,examples. In particular, we apply our method to a benchmark problem in multivariate robust control. By constructing a controller satisfying all design specifications but having only half the McMillan degree of conventional H-infinity controllers, we demonstrate the advantage of the proposed method.

  • 81.
    Lindquist, Anders
    et al.
    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, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Avventi, Enrico
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Graphical Models of Autoregressive Moving-Average ProcessesIn: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523Article in journal (Other academic)
  • 82.
    Lindquist, Anders G.
    et al.
    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, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Picci, Giorgio
    The Circulant Rational Covariance Extension Problem: The Complete Solution2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 11, p. 2848-2861Article in journal (Refereed)
    Abstract [en]

    The rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite-dimensional positive-definite Toeplitz matrix the northwest corner of which is given. The circulant rational covariance extension problem considered in this paper is a modification of this problem to partial stochastic realization of periodic stationary process, which are better represented on the discrete unit circle Z(2N) rather than on the discrete real line Z. The corresponding matrix completion problem then amounts to completing a finite-dimensional Toeplitz matrix that is circulant. Another important motivation for this problem is that it provides a natural approximation, involving only computations based on the fast Fourier transform, for the ordinary rational covariance extension problem, potentially leading to an efficient numerical procedure for the latter. The circulant rational covariance extension problem is an inverse problem with infinitely many solutions in general, each corresponding to a bilateral ARMA representation of the underlying periodic process. In this paper, we present a complete smooth parameterization of all solutions and convex optimization procedures for determining them. A procedure to determine which solution that best matches additional data in the form of logarithmic moments is also presented.

  • 83.
    Liu, Kun
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Fridman, Emilia
    Tel Aviv University.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Networked control with stochastic scheduling2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, no 99Article in journal (Refereed)
    Abstract [en]

    This paper develops the time-delay approach to networked control systems with scheduling protocols, variable delays and variable sampling intervals. The scheduling of sensor communication is defined by a stochastic protocol. Two classes of protocols are considered. The first one is defined by an independent and identically-distributed stochastic process. The activation probability of each sensor node for this protocol is a given constant, whereas it is assumed that collisions occur with a certain probability. The resulting closed-loop system is a stochastic impulsive system with delays both in the continuous dynamics and in the reset equations, where the system matrices have stochastic parameters with Bernoulli distributions. The second scheduling protocol is defined by a discrete-time Markov chain with a known transition probability matrix taking into account collisions. The resulting closed-loop system is a Markovian jump impulsive system with delays both in the continuous dynamics and in the reset equations. Sufficient conditions for exponential mean-square stability of the resulting closed-loop system are derived via a Lyapunov-Krasovskii-based method. The efficiency of the method is illustrated on an example of a batch reactor. It is demonstrated how the time-delay approach allows treating network-induced delays larger than the sampling intervals in the presence of collisions.

  • 84. Lou, Y.
    et al.
    Hong, Y.
    Xie, L.
    Shi, G.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Nash equilibrium computation in subnetwork zero-sum games with switching communications2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 10, p. 2920-2935, article id 7345550Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate a distributed Nash equilibrium computation problem for a time-varying multi-agent network consisting of two subnetworks, where the two subnetworks share the same objective function. We first propose a subgradientbased distributed algorithm with heterogeneous stepsizes to compute a Nash equilibrium of a zero-sum game. We then prove that the proposed algorithm can achieve a Nash equilibrium under uniformly jointly strongly connected (UJSC) weight-balanced digraphs with homogenous stepsizes. Moreover, we demonstrate that for weighted-unbalanced graphs a Nash equilibrium may not be achieved with homogenous stepsizes unless certain conditions on the objective function hold. We show that there always exist heterogeneous stepsizes for the proposed algorithm to guarantee that a Nash equilibrium can be achieved for UJSC digraphs. Finally, in two standard weight-unbalanced cases, we verify the convergence to a Nash equilibrium by adaptively updating the stepsizes along with the arc weights in the proposed algorithm. © 2015 IEEE.

  • 85. Lou, Youcheng
    et al.
    Shi, Guodong
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hong, Yiguang
    Approximate Projected Consensus for Convex Intersection Computation: Convergence Analysis and Critical Error Angle2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 7, p. 1722-1736Article in journal (Refereed)
    Abstract [en]

    In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that pi/4 is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations.

  • 86. Lygeros, J.
    et al.
    Johansson, Karl H.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Simic, S. N.
    Zhang, J.
    Sastry, S. S.
    Dynamical properties of hybrid automata2003In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 48, no 1, p. 2-17Article in journal (Refereed)
  • 87. Macellari, Luca
    et al.
    Karayiannidis, Yiannis
    KTH, School of Computer Science and Communication (CSC), Robotics, perception and learning, RPL.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Multi-Agent Second Order Average Consensus With Prescribed Transient Behavior2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 10, p. 5282-5288Article in journal (Refereed)
  • 88.
    Magnusson, Sindri
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Network and Systems engineering. KTH - Royal Institute of Technology.
    Enyioha, Chinwendu
    Li, Na
    Carlo, Fischione
    KTH, School of Electrical Engineering and Computer Science (EECS), Network and Systems engineering.
    Tarokh, Vahid
    Convergence of Limited Communication Gradient Methods2018In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 5, p. 1356-1371Article in journal (Refereed)
    Abstract [en]

    Distributed optimization increasingly plays a centralrole in economical and sustainable operation of cyber-physicalsystems. Nevertheless, the complete potential of the technologyhas not yet been fully exploited in practice due to communicationlimitations posed by the real-world infrastructures. This workinvestigates fundamental properties of distributed optimizationbased on gradient methods, where gradient information iscommunicated using limited number of bits. In particular, ageneral class of quantized gradient methods are studied wherethe gradient direction is approximated by a finite quantizationset. Sufficient and necessary conditions are provided on sucha quantization set to guarantee that the methods minimize anyconvex objective function with Lipschitz continuous gradient anda nonempty and bounded set of optimizers. A lower bound on thecardinality of the quantization set is provided, along with specificexamples of minimal quantizations. Convergence rate results areestablished that connect the fineness of the quantization andthe number of iterations needed to reach a predefined solutionaccuracy. Generalizations of the results to a relevant class ofconstrained problems using projections are considered. Finally,the results are illustrated by simulations of practical systems.

  • 89.
    Markdahl, Johan
    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.
    Kragic, Danica
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Karayiannidis, Yiannis
    A Hybrid Control Approach to Task-Priority Based Mobile ManipulationIn: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523Article in journal (Refereed)
  • 90. Meng, Z.
    et al.
    Xia, W.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hirche, S.
    Stability of Positive Switched Linear Systems: Weak Excitation and Robustness to Time-Varying Delay2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 1, p. 399-405, article id 7409998Article in journal (Refereed)
    Abstract [en]

    This article investigates the stability of positive switched linear systems. We start from motivating examples and focus on the case when each switched subsystem is marginally stable (in the sense that all the eigenvalues of the subsystem matrix are in the closed left-half plane with those on the imaginary axis simple) instead of asymptotically stable. A weak excitation condition is first proposed such that the considered positive switched linear system is exponentially stable. An extension to the case without dwell time assumption is also presented. Then, we study the influence of time-varying delay on the stability of the considered positive switched linear system. We show that the proposed weak excitation condition for the delay-free case is also sufficient for the asymptotic stability of the positive switched linear system under unbounded time-varying delay. In addition, it is shown that the convergence rate is exponential if there exists an upper bound for the delay, irrespective of the magnitude of this bound. The motivating examples are revisited to illustrate the theoretical results.

  • 91.
    Meyer, Pierre-Jean
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Girard, Antoine
    Univ Paris Sud, Lab Signaux & Systemes, CNRS, CentraleSupelec, F-91192 Gif Sur Yvette, France..
    Witrant, Emmanuel
    Univ Grenoble, CNRS, GIPSA Lab, F-38000 Grenoble, France..
    Compositional Abstraction and Safety Synthesis Using Overlapping Symbolic Models2018In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 6, p. 1835-1841Article in journal (Refereed)
    Abstract [en]

    In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete-time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using nonoverlapping subsystems.

  • 92.
    Molin, Adam
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hirche, Sandra
    Event-Triggered State Estimation: An Iterative Algorithm and Optimality Properties2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 11, p. 5939-5946Article in journal (Refereed)
    Abstract [en]

    This paper investigates the optimal design of event-triggered estimation for linear systems. The synthesis approach is posed as a team decision problem where the decision makers are given by the event trigger and the estimator. The event-trigger decides upon its available measurements whether the estimator shall obtain the current state information by transmitting it through a resource constrained channel. The objective is to find the optimal tradeoff between the mean square estimation error and the expected number of transmissions over a finite horizon. After deriving basic characteristics of the optimal solution, we propose an iterative algorithm that alternates between optimizing one decision maker while fixing the other and vice versa. By analyzing the dynamical behavior of the iterative method, it is shown that the algorithm converges to a symmetric threshold policy for first-order systems if the statistics of the uncertainties are even and unimodal. In the case of bimodal distributions, we show numerically that the iterative method may find asymmetric threshold policies that outperform symmetric rules.

  • 93.
    Mårtensson, Jonas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    How to Make Bias and Variance Errors Insensitive to System and Model Complexity in Identification2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 1, p. 100-112Article in journal (Refereed)
    Abstract [en]

    Solutions to optimal input design problems for system identification are sometimes believed to be sensitive to the underlying assumptions. For example, a wide class of problems can be solved with sinusoidal inputs with the same number of excitation frequencies (over the frequency range (-pi, pi]) as the number of model parameters. The order of the true system is in many cases unknown and, hence, so is the required number of frequencies in the input. In this contribution we characterize when and how the input spectrum can be chosen so that the (asymptotic) variance error of a scalar function of the model parameters becomes independent of the order of the true system. A connection between these robust designs and the solutions of certain optimal input design problems is also made. Furthermore, we show that there are circumstances when using this type of input allows some model properties to be estimated consistently even when the model order is lower than the order of the true system. The results are derived under the assumptions of causal linear time invariant systems operating in open loop and excited by an input signal having a rational spectral factor with all poles and zeros strictly inside the unit circle.

  • 94.
    Möller, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Input-Output Analysis of Power Control in Wireless Networks2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 4, p. 834-846Article in journal (Refereed)
    Abstract [en]

    In a wireless communication network, different users share a common resource. An objective of radio resource management is to assign the resources in an effective way among the users. Power control is an important component in this setting that has been extensively studied over the last two decades. In many real networks, there are inherent time delays due to filtering of signals and control signalling. Time delays can affect stability and convergence properties of the power control algorithms. We therefore consider power control laws of higher order to include models with delays and delay compensation. The main contribution of this paper is to exploit more structure of the interference feedback to prove less conservative conditions for system stability. Our primary tool to reduce conservativeness is to use scalings in an input-output framework for stability analysis.

  • 95.
    Ninness, B.
    et al.
    University of Newcastle.
    Hjalmarsson, Håkan
    KTH, Superseded Departments, Signals, Sensors and Systems.
    The effect of regularization on variance error2004In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 49, no 7, p. 1142-1147Article in journal (Refereed)
    Abstract [en]

    This note addresses the problem of quantifying the effect of noise induced error(so called variance error) in system estimates found via a regularised cost criterion. It builds on recent work by the authors in which expressions for nonregularised criterions are derived which are exact for finite model order. Those new expressions were established to be very different to previous quantifications that are widely used but based on asymptotic in model order arguments. A key purpose of this note is to expose a rapprochement between these new finite model order, and the preexisting asymptotic model order quantifications. In so doing, a further new result is established. Namely, that variance error in the frequency domain is dependent on the choice of the point about which regularization is affected.

  • 96.
    Ninness, Brett
    et al.
    University of Newcastle.
    Hjalmarsson, Håkan
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Variance error quantifications that are exact for finite-model order2004In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 49, no 8, p. 1275-1291Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of improved accuracy, this paper provides new expressions whose accuracy depends only on data length. They are therefore exact for arbitrarily small true model order. Other authors have recognized the importance of such expressions and have derived them for the case of finite-impulse response-like model structures in which denominators are fixed at true values and only numerator terms are estimated. This paper progresses beyond this situation to address the more general output-error and Box-Jenkins structures in which full dynamics models (both numerator and denominator terms) and noise models may be estimated. A key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed.

  • 97. Quevedo, Daniel
    et al.
    Ahlén, Anders
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    State Estimation Over Sensor Networks With Correlated Wireless Fading Channels2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 3, p. 581-593Article in journal (Refereed)
    Abstract [en]

    Stochastic stability for centralized time-varying Kalman filtering over a wireless sensor network with correlated fading channels is studied. On their route to the gateway, sensor packets, possibly aggregated with measurements from several nodes, may be dropped because of fading links. To study this situation, we introduce a network state process, which describes a finite set of configurations of the radio environment. The network state characterizes the channel gain distributions of the links, which are allowed to be correlated between each other. Temporal correlations of channel gains are modeled by allowing the network state process to form a (semi-)Markov chain. We establish sufficient conditions that ensure the Kalman filter to be exponentially bounded. In the one-sensor case, this new stability condition is shown to include previous results obtained in the literature as special cases. The results also hold when using power and bit-rate control policies, where the transmission power and bit-rate of each node are nonlinear mapping of the network state and channel gains.

  • 98.
    Ramesh, Chithrupa
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Design of State-Based Schedulers for a Network of Control Loops2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 8, p. 1962-1975Article in journal (Refereed)
    Abstract [en]

    For a closed-loop system with a contention-based multiple access network on its sensor link, the medium access controller (MAC) may discard some packets when the traffic on the link is high. We use a local state-based scheduler to select a few critical data packets to send to the MAC. In this paper, we analyze the impact of such a scheduler on the closed-loop system in the presence of traffic, and show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of an innovations-based scheduler with a certainty equivalent controller. However, this controller is not an equivalent design for the optimal controller, in the sense of Witsenhausen. The computation of the estimate can be simplified by introducing a symmetry constraint on the scheduler. Based on these findings, we propose a dual predictor architecture for the closed-loop system, which ensures separation between scheduler, observer and controller. We present an example of this architecture, which illustrates a network-aware event-triggering mechanism.

  • 99. Ramesh, Chithrupa
    et al.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Performance Analysis of a Network of Event-Based Systems2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 11, p. 3568-3573Article in journal (Refereed)
    Abstract [en]

    We consider a scenario where multiple event-based systems use a contention resolution mechanism (CRM) to communicate with their respective controllers over a wireless network. We present a Markov model that captures the joint interactions of the event-triggering policy and the CRM. This model is obtained by decoupling interactions between the different systems in the network, drawing inspiration from Bianchi's analysis of IEEE 802.11. We present Monte-Carlo simulations that validate our model under various network configurations, and verify the accuracy of the performance analysis.

  • 100.
    Ren, Wei
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Xiong, Junlin
    Univ Sci & Technol China, Dept Automat, Hefei 230026, Anhui, Peoples R China..
    Stability Analysis of Impulsive Switched Time-Delay Systems With State-Dependent Impulses2019In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 64, no 9, p. 3928-3935Article in journal (Refereed)
    Abstract [en]

    This paper studies the stability for impulsive switched time-delay systems with state-dependent impulses. Since the impulses and the switches are not necessarily synchronous, we start from a stability analysis of impulsive switched time-delay systems with time-dependent impulses. Sufficient conditions are derived to guarantee the stability property, which extends the previous results for the synchronous switch and impulse case. For the state-dependent impulse case, using the B-equivalent method, impulsive switched time-delay systems with state-dependent impulses are transformed into impulsive switched time-delay systems with time-dependent impulses. The equivalence between the original system and the transformed system is established, and stability conditions are obtained for impulsive switched time-delay systems with state-dependent impulses. Finally, a numerical example is given to demonstrate the obtained results.

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