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  • 1.
    Abdalmoaty, Mohamed R.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Linear Prediction Error Methods for Stochastic Nonlinear Models2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, p. 49-63Article in journal (Refereed)
    Abstract [en]

    The estimation problem for stochastic parametric nonlinear dynamical models is recognized to be challenging. The main difficulty is the intractability of the likelihood function and the optimal one-step ahead predictor. In this paper, we present relatively simple prediction error methods based on non-stationary predictors that are linear in the outputs. They can be seen as extensions of the linear identification methods for the case where the hypothesized model is stochastic and nonlinear. The resulting estimators are defined by analytically tractable objective functions in several common cases. It is shown that, under certain identifiability and standard regularity conditions, the estimators are consistent and asymptotically normal. We discuss the relationship between the suggested estimators and those based on second-order equivalent models as well as the maximum likelihood method. The paper is concluded with a numerical simulation example as well as a real-data benchmark problem.

    The full text will be freely available from 2021-04-01 16:05
  • 2.
    Agüero, Juan C.
    et al.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    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.
    Goodwin, Graham C.
    The University of Newcastle, Australia.
    Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 4, p. 632-637Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.

  • 3.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Harmonic analysis of pulse-width modulated systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 4, p. 851-862Article in journal (Refereed)
    Abstract [en]

    The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class switching systems. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback. The dynamic phasor model is a powerful tool for exploring cyclic properties of dynamic systems. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems.

  • 4. Anderson, R. P.
    et al.
    Milutinović, D.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Self-triggered sampling for second-moment stability of state-feedback controlled SDE systems2015In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 54, p. 8-15Article in journal (Refereed)
    Abstract [en]

    Event-triggered and self-triggered control, whereby the times for controller updates are computed from sampled data, have recently been shown to reduce the computational load or increase task periods for real-time embedded control systems. In this work, we propose a self-triggered scheme for nonlinear controlled stochastic differential equations with additive noise terms. We find that the family of trajectories generated by these processes demands a departure from the standard deterministic approach to event- and self-triggering, and, for that reason, we use the statistics of the sampled-data system to derive a self-triggering update condition that guarantees second-moment stability. We show that the length of the times between controller updates as computed from the proposed scheme is strictly positive and provide related examples.

  • 5. Aragues, Rosario
    et al.
    Shi, Guodong
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Saguees, Carlos
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mezouar, Youcef
    Distributed algebraic connectivity estimation for undirected graphs with upper and lower bounds2014In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, no 12, p. 3253-3259Article in journal (Refereed)
    Abstract [en]

    The algebraic connectivity of the graph Laplacian plays an essential role in various multi-agent control systems. In many cases a lower bound of this algebraic connectivity is necessary in order to achieve a certain performance. Lately, several methods based on distributed Power Iteration have been proposed for computing the algebraic connectivity of a symmetric Laplacian matrix. However, these methods cannot give any lower bound of the algebraic connectivity and their convergence rates are often unclear. In this paper, we present a distributed algorithm for estimating the algebraic connectivity for undirected graphs with symmetric Laplacian matrices. Our method relies on the distributed computation of the powers of the adjacency matrix and its main interest is that, at each iteration, agents obtain both upper and lower bounds for the true algebraic connectivity. Both bounds successively approach the true algebraic connectivity with the convergence speed no slower than O(1/k).

  • 6.
    Barenthin, Märta
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bombois, Xavier
    TU Delft.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Scorletti, Gerard
    Ecole Centrale de Lyon.
    Identification for control of multivariable systems: Controller validation and experiment design via LMIs2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 12, p. 3070-3078Article in journal (Refereed)
    Abstract [en]

    This paper presents a new controller validation method for linear multivariable time-invariant models. Classical prediction error system identification methods deliver uncertainty regions which are nonstandard in the robust control literature. Our controller validation criterion computes an upper bound for the worst case performance, measured in terms of the H-infinity-norm of a weighted closed loop transfer matrix, achieved by a given controller over all plants in such uncertainty sets. This upper bound on the worst case performance is computed via an LMI-based optimization problem and is deduced via the separation of graph framework. Our main technical contribution is to derive, within that framework, a very general parametrization for the set of multipliers corresponding to the nonstandard uncertainty regions resulting from PE identification of MIMO systems. The proposed approach also allows for iterative experiment design. The results of this paper are asymptotic in the data length and it is assumed that the model structure is flexible enough to capture the true system.

  • 7.
    Barenthin, Märta
    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.
    Identification and control: Joint input design and H-infinity state feedback with ellipsoidal parametric uncertainty via LMIs2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 2, p. 543-551Article in journal (Refereed)
    Abstract [en]

    One obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods. In this contribution we present a joint robust state feedback control/input design procedure which guarantees stability and prescribed closed-loop performance using models identified from experimental data. This means that given H-infinity specifications on the closed-loop transfer function are translated into sufficient requirements on the input signal spectrum used to identify the process. The condition takes the form of a linear matrix inequality.

  • 8.
    Beerens, R.
    et al.
    Eindhoven Univ Technol, Dept Mech Engn, NL-5600 MB Eindhoven, Netherlands..
    Bisoffi, Andrea
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Zaccarian, L.
    Univ Toulouse, LAAS, CNRS, F-31400 Toulouse, France.;Univ Trento, I-38122 Trento, Italy..
    Heemels, W. P. M. H.
    Eindhoven Univ Technol, Dept Mech Engn, NL-5600 MB Eindhoven, Netherlands..
    Nijmeijer, H.
    Eindhoven Univ Technol, Dept Mech Engn, NL-5600 MB Eindhoven, Netherlands..
    van de Wouw, N.
    Eindhoven Univ Technol, Dept Mech Engn, NL-5600 MB Eindhoven, Netherlands.;Univ Minnesota, Civil Environm & Geoengn Dept, Minneapolis, MN 55455 USA..
    Reset integral control for improved settling of PID-based motion systems with friction2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 107, p. 483-492Article in journal (Refereed)
    Abstract [en]

    We present a reset control approach to improve the transient performance of a PID-controlled motion system subject to Coulomb and viscous friction. A reset integrator is applied to circumvent the depletion and refilling process of a linear integrator when the solution overshoots the setpoint, thereby significantly reducing the settling time. Robustness for unknown static friction levels is obtained. The closed-loop system is formulated through a hybrid systems framework, within which stability is proven using a discontinuous Lyapunov-like function and a meagre-limsup invariance argument. The working principle of the proposed reset controller is analyzed in an experimental benchmark study of an industrial high-precision positioning machine.

  • 9.
    Berkane, Soulaimane
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Tayebi, A.
    Attitude estimation with intermittent measurements2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, p. 415-421Article in journal (Refereed)
    Abstract [en]

    We propose a framework for attitude estimation on the Special Orthogonal group SO(3) using intermittent body-frame vector measurements. We consider the case where the vector measurements are synchronously-intermittent (all measurements are received at the same time) and the case where the vector measurements are asynchronously-intermittent (not all measurements are received at the same time). The proposed observers have a measurement-triggered structure where the attitude is predicted using the continuously measured angular velocity when the vector measurements are not available, and adequately corrected upon the arrival of the vector measurements. A hybrid framework is proposed to capture the behaviour of the closed-loop system by extending the state with timers that are reset at each jump of the observer state. Almost global asymptotic stability is shown using rigorous Lyapunov techniques for hybrid systems.

  • 10.
    Bishop, Adrian N.
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Fidan, Baris
    Anderson, Brian D. O.
    Dogancay, Kutluyil
    Pathirana, Pubudu N.
    Optimality analysis of sensor-target localization geometries2010In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, no 3, p. 479-492Article in journal (Refereed)
    Abstract [en]

    The problem of target localization involves estimating the position of a target from multiple noisy sensor measurements. It is well known that the relative sensor-target geometry can significantly affect the performance of any particular localization algorithm. The localization performance can be explicitly characterized by certain measures, for example, by the Cramer-Rao lower bound (which is equal to the inverse Fisher information matrix) on the estimator variance. In addition, the Cramer-Rao lower bound is commonly used to generate a so-called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate, i.e. an estimate which achieves the lower bound. The aim of this work is to identify those relative sensor-target geometries which result in a measure of the uncertainty ellipse being minimized. Deeming such sensor-target geometries to be optimal with respect to the chosen measure, the optimal sensor-target geometries for range-only, time-of-arrival-based and bearing-only localization are identified and studied in this work. The optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor-target configuration is not, in general, unique. The importance of understanding the influence of the sensor-target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples.

  • 11. Boem, F.
    et al.
    Zhou, Y.
    Fischione, Carlo
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Parisini, T.
    Distributed Pareto-optimal state estimation using sensor networks2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 93, p. 211-223Article in journal (Refereed)
    Abstract [en]

    A novel model-based dynamic distributed state estimator is proposed using sensor networks. The estimator consists of a filtering step – which uses a weighted combination of information provided by the sensors – and a model-based predictor of the system's state. The filtering weights and the model-based prediction parameters jointly minimize – at each time-step – the bias and the variance of the prediction error in a Pareto optimization framework. The simultaneous distributed design of the filtering weights and of the model-based prediction parameters is considered, differently from what is normally done in the literature. It is assumed that the weights of the filtering step are in general unequal for the different state components, unlike existing consensus-based approaches. The state, the measurements, and the noise components are allowed to be individually correlated, but no probability distribution knowledge is assumed for the noise variables. Each sensor can measure only a subset of the state variables. The convergence properties of the mean and of the variance of the prediction error are demonstrated, and they hold both for the global and the local estimation errors at any network node. Simulation results illustrate the performance of the proposed method, obtaining better results than state of the art distributed estimation approaches.

  • 12. Bombois, X.
    et al.
    Korniienko, A.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Scorletti, G.
    Optimal identification experiment design for the interconnection of locally controlled systems2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, p. 169-179Article in journal (Refereed)
    Abstract [en]

    This paper considers the identification of the modules of a network of locally controlled systems (multi-agent systems). Its main contribution is to determine the least perturbing identification experiment that will nevertheless lead to sufficiently accurate models of each module for the global performance of the network to be improved by a redesign of the decentralized controllers. Another contribution is to determine the experimental conditions under which sufficiently informative data (i.e. data leading to a consistent estimate) can be collected for the identification of any module in such a network. 

  • 13.
    Bombois, Xavier
    et al.
    TU Delft.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Scorletti, Gerard
    Ecole Centrale de Lyon.
    Identification for robust H-2 deconvolution filtering2010In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, no 3, p. 577-584Article in journal (Refereed)
    Abstract [en]

    This paper addresses robust deconvolution filtering when the system and noise dynamics are obtained by parametric system identification. Consistent with standard identification methods, the uncertainty in the estimated parameters is represented by an ellipsoidal uncertainty region. Three problems are considered: (1) computation of the worst case H-2 performance of a given deconvolution filter in this uncertainty set; (2) design of a filter which minimizes the worst case H-2 performance in this uncertainty set; (3) input design for the identification experiment, subject to a limited input power budget, such that the filter in (2) gives the smallest possible worst case H-2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to (1) and (2) while the third problem can be treated via iterating between two convex optimization problems.

  • 14.
    Bottegal, Giulio
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Aravkin, Aleksandr Y.
    Hjalmarsson, Hakan
    Pillonetto, Gianluigi
    Robust EM kernel-based methods for linear system identification2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 67, p. 114-126Article in journal (Refereed)
    Abstract [en]

    Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robustify kernel-based system identification methods. To this end, we model the output measurement noise using random variables with heavy-tailed probability density functions (pdfs), focusing on the Laplacian and the Student's t distributions. Exploiting the representation of these pdfs as scale mixtures of Gaussians, we cast our system identification problem into a Gaussian process regression framework, which requires estimating a number of hyperparameters of the data size order. To overcome this difficulty, we design a new maximum a posteriori (MAP) estimator of the hyperparameters, and solve the related optimization problem with a novel iterative scheme based on the Expectation-Maximization (EM) method. In the presence of outliers, tests on simulated data and on a real system show a substantial performance improvement compared to currently used kernel-based methods for linear system identification. (C) 2016 Elsevier Ltd. All rights reserved.

  • 15. Bottegal, Giulio
    et al.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pillonetto, Gianluigi
    A new kernel-based approach to system identification with quantized output data2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 85, p. 145-152Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data. (C) 2017 Elsevier Ltd. All rights reserved.

  • 16. Cantoni, M.
    et al.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Computing the L-2 gain for linear periodic continuous-time systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 3, p. 783-789Article in journal (Refereed)
    Abstract [en]

    A method to compute the L-2 gain is developed for the class of linear periodic continuous-time systems that admit a finite-dimensional state-space realisation. A bisection search for the smallest upper bound on the gain is employed, where at each step an equivalent discrete-time problem is considered via the well known technique of time-domain lifting. The equivalent problem involves testing a bound on the gain of a linear shift-invariant discrete-time system, with the same state dimension as the periodic continuous-time system. It is shown that a state-space realisation of the discrete-time system can be constructed from point solutions to a linear differential equation and two differential Riccati equations, all subject to only single-point boundary conditions. These are well behaved over the corresponding one period intervals of integration, and as such, the required point solutions can be computed via standard methods for ordinary differential equations. A numerical example is presented and comparisons made with alternative techniques.

  • 17. Carli, Ruggero
    et al.
    Fagnani, Fabio
    Speranzon, Alberto
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Zampieri, Sandro
    Communication constraints in the average consensus problem2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 3, p. 671-684Article in journal (Refereed)
    Abstract [en]

    The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that time-invariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly time-varying communication networks allow very fast convergence rates. We also show that by adding logarithmic quantized data links to time-invariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.

  • 18.
    Carvalho, J. Frederico
    et al.
    KTH, School of Computer Science and Communication (CSC), Robotics, perception and learning, RPL. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Pequito, S.
    Aguiar, A. P.
    Kar, S.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Composability and controllability of structural linear time-invariant systems: Distributed verification2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 78, p. 123-134Article in journal (Refereed)
    Abstract [en]

    Motivated by the development and deployment of large-scale dynamical systems, often comprised of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. Specifically, we study controllability in the structural system theoretic sense, structural controllability, in which rather than focusing on a specific numerical system realization, we provide guarantees for equivalence classes of linear time-invariant systems on the basis of their structural sparsity patterns, i.e., the location of zero/nonzero entries in the plant matrices. Towards this goal, we first provide several necessary and/or sufficient conditions that ensure that the overall system is structurally controllable on the basis of the subsystems’ structural pattern and their interconnections. The proposed verification criteria are shown to be efficiently implementable (i.e., with polynomial time-complexity in the number of the state variables and inputs) in two important subclasses of interconnected dynamical systems: similar (where every subsystem has the same structure) and serial (where every subsystem outputs to at most one other subsystem). Secondly, we provide an iterative distributed algorithm to verify structural controllability for general interconnected dynamical system, i.e., it is based on communication among (physically) interconnected subsystems, and requires only local model and interconnection knowledge at each subsystem.

  • 19. Dai, L.
    et al.
    Gao, Yulong
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Xie, L.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Xia, Y.
    Stochastic self-triggered model predictive control for linear systems with probabilistic constraints2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 92, p. 9-17Article in journal (Refereed)
    Abstract [en]

    A stochastic self-triggered model predictive control (SSMPC) algorithm is proposed for linear systems subject to exogenous disturbances and probabilistic constraints. The main idea behind the self-triggered framework is that at each sampling instant, an optimization problem is solved to determine both the next sampling instant and the control inputs to be applied between the two sampling instants. Although the self-triggered implementation achieves communication reduction, the control commands are necessarily applied in open-loop between sampling instants. To guarantee probabilistic constraint satisfaction, necessary and sufficient conditions are derived on the nominal systems by using the information on the distribution of the disturbances explicitly. Moreover, based on a tailored terminal set, a multi-step open-loop MPC optimization problem with infinite prediction horizon is transformed into a tractable quadratic programming problem with guaranteed recursive feasibility. The closed-loop system is shown to be stable. Numerical examples illustrate the efficacy of the proposed scheme in terms of performance, constraint satisfaction, and reduction of both control updates and communications with a conventional time-triggered scheme.

  • 20. Delellis, P.
    et al.
    Di Bernardo, M.
    Liuzza, Davide
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, Italy.
    Convergence and synchronization in heterogeneous networks of smooth and piecewise smooth systems2015In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 56, p. 1-11Article in journal (Refereed)
    Abstract [en]

    This paper presents a framework for the study of convergence in networks where the nodes’ dynamics may be both piecewise smooth and/or nonidentical. Sufficient conditions are derived for global convergence of all node trajectories towards the same bounded region in the synchronization error space. The analysis is based on the use of set-valued Lyapunov functions and bounds are derived on the minimum coupling strength required to make all nodes in the network converge towards each other. We also provide an estimate of the asymptotic bound on the mismatch between the node state trajectories. The analysis is performed both for linear and nonlinear coupling protocols. The theoretical analysis is extensively illustrated and validated via its application to a set of representative numerical examples.

  • 21.
    Dimarogonas, Dimos V.
    et al.
    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.
    Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control2010In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, no 4, p. 695-700Article in journal (Refereed)
    Abstract [en]

    The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.

  • 22.
    Dimarogonas, Dimos V.
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Kyriakopoulos, K. J.
    A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 10, p. 2648-2654Article in journal (Refereed)
    Abstract [en]

    In this paper, a feedback control strategy that achieves convergence of a multi-agent system to a desired formation configuration is proposed for both the cases of agents with single integrator and nonholonomic unicycle-type kinematics. When inter-agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible. it is shown that under certain assumptions, formation infeasibility forces the agents' velocity vectors to a common value at steady state. This provides a connection between formation infeasibility and flocking behavior for the multi-agent system. We finally also obtain an analytic expression of the common velocity vector in the case of formation infeasibility.

  • 23. Duerr, Hans-Bernd
    et al.
    Stankovic, Milos S.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ebenbauer, Christian
    Extremum seeking on submanifolds in the Euclidian space2014In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, no 10, p. 2591-2596Article in journal (Refereed)
    Abstract [en]

    Extremum seeking is a powerful control method to steer a dynamical system to an extremum of a partially unknown function. In this paper, we introduce extremum seeking systems on submanifolds in the Euclidian space. Using a trajectory approximation technique based on Lie brackets, we prove that uniform asymptotic stability of the so-called Lie bracket system on the manifold implies practical uniform asymptotic stability of the corresponding extremum seeking system on the manifold. We illustrate the approach with an example of extremum seeking on a torus.

  • 24. Dürr, Hans-Bernd
    et al.
    Stankovic, Milos S.
    Ebenbauer, Christian
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Lie bracket approximation of extremum seeking systems2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 6, p. 1538-1552Article in journal (Refereed)
    Abstract [en]

    Extremum seeking feedback is a powerful method to steer a dynamical system to an extremum of a partially or completely unknown map. It often requires advanced system-theoretic tools to understand the qualitative behavior of extremum seeking systems. In this paper, a novel interpretation of extremum seeking is introduced. We show that the trajectories of an extremum seeking system can be approximated by the trajectories of a system which involves certain Lie brackets of the vector fields of the extremum seeking system. It turns out that the Lie bracket system directly reveals the optimizing behavior of the extremum seeking system. Furthermore, we establish a theoretical foundation and prove that uniform asymptotic stability of the Lie bracket system implies practical uniform asymptotic stability of the corresponding extremum seeking system. We use the established results in order to prove local and semi-global practical uniform asymptotic stability of the extrema of a certain map for multi-agent extremum seeking systems.

  • 25. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Cost function shaping of the output error criterion2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 76, p. 53-60Article in journal (Refereed)
    Abstract [en]

    Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because in most cases both the corresponding objective function and the search space are nonconvex. The difficulty in solving the optimization problem depends mainly on the experimental conditions, more specifically on the spectra of the input/output data collected from the system. It is therefore possible to improve the convergence of the algorithms by properly choosing the data prefilters; in this paper we show how to perform this choice. We present the application of the proposed approach to case studies where the standard algorithms tend to fail to converge to the global minimum.

  • 26. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    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.
    Input design as a tool to improve the convergence of PEM2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 11, p. 3282-3291Article in journal (Refereed)
    Abstract [en]

    The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The shape of the cost function, and hence the difficulty in solving the optimization problem, depends directly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. Therefore, it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input; in this paper, we address this problem. We present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design. We present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima.

  • 27. Esparza, Alicia
    et al.
    Agüero, Juan C.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Godoy, Boris I.
    The University of Newcastle, Australia.
    Asymptotic statistical analysis for model-based control design strategies2011In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, no 5, p. 1041-1046Article in journal (Refereed)
    Abstract [en]

    In this paper, we generalize existing fundamental limitations on the accuracy of the estimation of dynamic models. In addition, we study the large sample statistical behavior of different estimation-based controller design strategies. In particular, fundamental limitations on the closed-loop performance using a controller obtained by Virtual Reference Feedback Tuning (VRFT) are studied. We also extend our results to more general estimation-based control design strategies. We present numerical examples to show the application of our results.

  • 28.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    Eindhoven Univ Technol, Dept Elect Engn, Eindhoven, Netherlands..
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    An empirical Bayes approach to identification of modules in dynamic networks2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 91, p. 144-151Article in journal (Refereed)
    Abstract [en]

    We present a new method of identifying a specific module in a dynamic network, possibly with feedback loops. Assuming known topology, we express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Additionally, we extend the method to include additional measurements downstream of the target module. Using Markov Chain Monte Carlo techniques, it is shown that the same iterative scheme can solve also this formulation. Numerical experiments illustrate the effectiveness of the proposed methods.

  • 29.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Galrinho, Miguel
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, p. 221-234Article in journal (Refereed)
    Abstract [en]

    In system identification, it is often difficult to use a physical intuition when choosing a noise model structure. The importance of this choice is that, for the prediction error method (PEM) to provide asymptotically efficient estimates, the model orders must be chosen according to the true system. However, if only the plant estimates are of interest and the experiment is performed in open loop, the noise model can be over-parameterized without affecting the asymptotic properties of the plant. The limitation is that, as PEM suffers in general from non-convexity, estimating an unnecessarily large number of parameters will increase the risk of getting trapped in local minima. Here, we consider the following alternative approach. First, estimate a high-order ARX model with least squares, providing non-parametric estimates of the plant and noise model. Second, reduce the high-order model to obtain a parametric model of the plant only. We review existing methods to do this, pointing out limitations and connections between them. Then, we propose a method that connects favorable properties from the previously reviewed approaches. We show that the proposed method provides asymptotically efficient estimates of the plant with open-loop data. Finally, we perform a simulation study suggesting that the proposed method is competitive with state-of-the-art methods.

  • 30.
    Fanizza, Giovanna
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Nagamune, Ryozo
    Univ British Columbia, Dept Mech Engn.
    Spectral estimation by least-squares optimization based on rational covariance extension2007In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, no 2, p. 362-370Article in journal (Refereed)
    Abstract [en]

    This paper proposes a new spectral estimation technique based on rational covariance extension with degree constraint. The technique finds a rational spectral density function that approximates given spectral density data under constraint on a covariance sequence. Spectral density approximation problems are formulated as nonconvex optimization problems with respect to a Schur polynomial. To formulate the approximation problems, the least-squares sum is considered as a distance. Properties of optimization problems and numerical algorithms to solve them are explained. Numerical examples illustrate how the methods discussed in this paper are useful in stochastic model reduction and stochastic process modeling.

  • 31.
    Farokhi, Farhad
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Langbort, Cedric
    Department of Aerospace Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Illinois, USA..
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 2, p. 326-337Article in journal (Refereed)
    Abstract [en]

    We introduce the family of limited model information control design methods, which construct controllers by accessing the plant's model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete-time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods which produce structured static state feedback controllers, where each subcontroller can at least access the state measurements of those subsystems that affect its corresponding subsystem. We compute the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. Finally, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.

  • 32.
    Farokhi, Farhad
    et al.
    CSIROs Data61, Canberra, ACT, Australia.; Univ Melbourne, Dept Elect & Elect Engn, Melbourne, Vic, Australia..
    Sandberg, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Ensuring privacy with constrained additive noise by minimizing Fisher information2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 99, p. 275-288Article in journal (Refereed)
    Abstract [en]

    The problem of preserving the privacy of individual entries of a database when responding to linear or nonlinear queries with constrained additive noise is considered. For privacy protection, the response to the query is systematically corrupted with an additive random noise whose support is a subset or equal to a pre-defined constraint set. A measure of privacy using the inverse of the trace of the Fisher information matrix is developed. The Cramer-Rao bound relates the variance of any estimator of the database entries to the introduced privacy measure. The probability density that minimizes the trace of the Fisher information (as a proxy for maximizing the measure of privacy) is computed. An extension to dynamic problems is also presented. Finally, the results are compared to the differential privacy methodology. Crown Copyright

  • 33. Farokhi, Farhad
    et al.
    Shames, Iman
    Rabbat, Michael G.
    Johansson, Mikael
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    On reconstructability of quadratic utility functions from the iterations in gradient methods2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 66, p. 254-261Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider a scenario where an eavesdropper can read the content of messages transmitted over a network. The nodes in the network are running a gradient algorithm to optimize a quadratic utility function where such a utility optimization is a part of a decision making process by an administrator. We are interested in understanding the conditions under which the eavesdropper can reconstruct the utility function or a scaled version of it and, as a result, gain insight into the decision-making process. We establish that if the parameter of the gradient algorithm, i.e., the step size, is chosen appropriately, the task of reconstruction becomes practically impossible for a class of Bayesian filters with uniform priors. We establish what step-size rules should be employed to ensure this. 

  • 34. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    LQ optimal control for a class of pulse width modulated systems2007In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, no 6, p. 1009-1020Article in journal (Refereed)
    Abstract [en]

    We consider linear quadratic optimal control for a class of pulse width modulated systems. The problem is motivated from a practical application-digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the intersampling behavior into account.

  • 35. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Robust tracking with H-infinity performance for PWM systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 8, p. 1808-1818Article in journal (Refereed)
    Abstract [en]

    Control synthesis for robust tracking is considered for a class of pulse-width modulated systems that appear, for example, in power electronics applications. The control objective is to regulate a high frequency ripple signal to robustly track a constant reference signal in an average sense. To achieve this goal, a new H-infinity control problem with integral action and average sampling is proposed. The solution of this problem involves a hybrid lifting framework which requires a careful elaboration in order to develop an algorithm that allows one to solve the design problem by the standard state space formulas for H-infinity control. The design procedure is verified on a synchronous buck converter.

  • 36.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Rojas, Cristián R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Estimating models with high-order noise dynamics using semi-parametric weighted null-space fitting2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 102, p. 45-57Article in journal (Refereed)
    Abstract [en]

    Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum. However, a too flexible noise model (i.e., too many parameters) increases the model complexity, which can cause additional numerical problems for PEM. In this paper, we consider the weighted null-space fitting (WNSF) method. With this method, the system is first modeled using a non-parametric ARX model, which is then reduced to a parametric model of interest using weighted least squares. In the reduction step, a parametric noise model does not need to be estimated if it is not of interest. Because the flexibility of the noise model is increased with the sample size, this will still provide consistent estimates in closed loop and asymptotically efficient estimates in open loop. In this paper, we prove these results, and we derive the asymptotic covariance for the estimation error obtained in closed loop, which is optimal for an infinite-order noise model. For this purpose, we also derive a new technical result for geometric variance analysis, instrumental to our end. Finally, we perform a simulation study to illustrate the benefits of the method when the noise model cannot be parametrized by a low-order model.

  • 37.
    Gao, Yulong
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Yu, Pian
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Xie, Lihua
    Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore..
    Robust self-triggered control for time-varying and uncertain constrained systems via reachability analysis2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 107, p. 574-581Article in journal (Refereed)
    Abstract [en]

    This paper develops a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. The resulting piecewise constant control inputs achieve communication reduction and guarantee constraint satisfactions. In the particular case when there is no uncertainty, we propose a control design with minimum number of samplings over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as computationally tractable mixed integer linear programs. The method is compared with the robust self-triggered model predictive control in a numerical example and applied to a robot motion planning problem with temporal constraints.

  • 38.
    Gerencser, Laszlo
    et al.
    Computer and Automation Institute of the Hungarian Academy of Sciences, (MTA SZTAKI),.
    Hjalmarsson, Håkan
    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.
    Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 3, p. 623-633Article in journal (Refereed)
    Abstract [en]

    A key problem in optimal input design is that the solution depends on system parameters to be identified. In this contribution we provide formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle, i.e. for each time step an optimal input design problem is solved exactly using the present parameter estimate and one sample of this input is applied to the system. The results apply to stable ARX systems with the input restricted to be generated by white noise filtered through a finite impulse response filter, or a binary signal obtained from the latter by a static nonlinearity.

  • 39.
    Ghandhari, Mehrdad
    et al.
    KTH, Superseded Departments, Electrical Systems.
    Andersson, G.
    Pavella, M.
    Ernst, D.
    A control strategy for controllable series capacitor in electric power systems2001In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 37, no 10, p. 1575-1583Article in journal (Refereed)
    Abstract [en]

    It has been verified that a controllable series capacitor with a suitable control scheme can improve transient stability and help to damp electromechanical oscillations. A question of great importance is the selection of the input signals and a control strategy for this device in order to damp power oscillations in an effective and robust manner. Based on Lyapunov theory a control strategy for damping of electromechanical power oscillations in a multi-machine power system is derived. Lyapunov theory deals with dynamical systems without inputs. For this reason, it has traditionally been applied only to closed-loop control systems, that is, systems for which the input has been eliminated through the substitution of a predetermined feedback control. However, in this paper, we use Lyapunov function candidates in feedback design itself by making the Lyapunov derivative negative when choosing the control. This control strategy is called control Lyapunov function for systems with control inputs. Also, two input signals for this control strategy are used. The first one is based on local information and the second one on remote information derived by the single machine equivalent method.

  • 40.
    Ghulchak, Andrey
    et al.
    Lund University, Department of Automatic Control.
    Sandberg, Henrik
    Lund University, Department of Automatic Control.
    Computer control systems. Analysis and design with process-oriented nodels: E. Rosenwasser and B. Lampe; Springer, London, 2000, ISBN 1-85233-307-32002In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 38, p. 2031-2035Article, book review (Other academic)
  • 41.
    Guo, Meng
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Consensus with quantized relative state measurements2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 8, p. 2531-2537Article in journal (Refereed)
    Abstract [en]

    In this paper, cooperative control of multi-agent systems under limited communication between neighboring agents is investigated. In particular, quantized values of the relative states are used as the control parameters. By taking advantage of tools from nonsmooth analysis, explicit convergence results are derived for both uniform and logarithmic quantizers under static and time-varying communication topologies. Compared with our previous work, less conservative conditions that ensure global convergence are provided. Moreover, second order dynamical systems under similar constraints are taken into account. Computer simulations are provided to demonstrate the validity of the derived results.

  • 42. Guo, Z.
    et al.
    Shi, D.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Shi, L.
    Worst-case stealthy innovation-based linear attack on remote state estimation2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, p. 117-124Article in journal (Refereed)
    Abstract [en]

    In this work, a security problem in cyber–physical systems is studied. We consider a remote state estimation scenario where a sensor transmits its measurement to a remote estimator through a wireless communication network. The Kullback–Leibler divergence is adopted as a stealthiness metric to detect system anomalies. We propose an innovation-based linear attack strategy and derive the remote estimation error covariance recursion in the presence of attack, based on which a two-stage optimization problem is formulated to investigate the worst-case attack policy. It is proved that the worst-case attack policy is zero-mean Gaussian distributed and the numerical solution is obtained by semi-definite programming. Moreover, an explicit algorithm is provided to calculate the compromised measurement. The trade-off between attack stealthiness and system performance degradation is evaluated via simulation examples. 

  • 43.
    Gustavi, Tove
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dimarogonas, Dimos V.
    Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, United States.
    Egerstedt, Magnus
    Hu, Xiaoming
    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 Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks2010In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, no 1, p. 133-139Article in journal (Refereed)
    Abstract [en]

    In this paper we derive a set of constraints that are sufficient to guarantee maintained connectivity in a leader-follower multi-agent network with proximity based communication topology. In the scenario we consider, only the leaders are aware of the global mission, which is to converge to a known destination point. Thus, the followers need to stay in contact with the group of leaders in order to reach the goal. In the paper we show that we can maintain the initial network structure, and thereby connectivity, by setting up bounds on the ratio of leaders-to-followers and on the magnitude of the goal attraction force experienced by the leaders. The results are first established for an initially complete communication graph and then extended to an incomplete graph. The results are illustrated by computer simulations.

  • 44.
    Ha, Huong
    et al.
    Univ Newcastle, Sch Elect Engn & Comp, Newcastle, NSW, Australia..
    Welsh, James S.
    Univ Newcastle, Sch Elect Engn & Comp, Newcastle, NSW, Australia..
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    An analysis of the SPARSEVA estimate for the finite sample data case2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 96, p. 141-149Article in journal (Refereed)
    Abstract [en]

    In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound of the estimation error for the traditional I-1 SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound. 

  • 45. Hashimoto, K.
    et al.
    Adachi, S.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Event-triggered intermittent sampling for nonlinear model predictive control2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 81, p. 148-155Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose a new aperiodic formulation of model predictive control for nonlinear continuous-time systems. Unlike earlier approaches, we provide event-triggered conditions without using the optimal cost as a Lyapunov function candidate. Instead, we evaluate the time interval when the optimal state trajectory enters a local set around the origin. The obtained event-triggered strategy is more suitable for practical applications than the earlier approaches in two directions. First, it does not include parameters (e.g., Lipschitz constant parameters of stage and terminal costs) which may be a potential source of conservativeness for the event-triggered conditions. Second, the event-triggered conditions are necessary to be checked only at certain sampling time instants, instead of continuously. This leads to the alleviation of the sensing cost and becomes more suitable for practical implementations under a digital platform. The proposed event-triggered scheme is also validated through numerical simulations.

  • 46.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    From experiment design to closed-loop control2005In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 41, no 3, p. 393-438Article in journal (Refereed)
    Abstract [en]

    The links between identification and control are examined. The main trends in this research area are summarized, with particular focus on the design of low complexity controllers from a statistical perspective. It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made as this ensures the best statistical accuracy. This does not necessarily mean that a full-order model always is necessary as well designed experiments allow for restricted complexity models to be near-optimal. Experiment design can therefore be seen as the key to successful applications. For this reason, particular attention is given to the interaction between experimental constraints and performance specifications.

  • 47.
    Hjalmarsson, Håkan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Jansson, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Closed loop experiment design for linear time invariant dynamical systems via LMIs2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 3, p. 623-636Article in journal (Refereed)
    Abstract [en]

    All stationary experimental conditions corresponding to a discrete-time linear time-invariant causal internally stable closed loop with real rational system and feedback controller are characterized using the Youla-Kucera parametrization. Finite dimensional parametrizations of the input spectrum and the Youla-Kucera parameter allow a wide range of closed loop experiment design problems, based on the asymptotic (in the sample size) covariance matrix for the estimated parameters, to be recast as computationally tractable convex optimization problems such as semi-definite programs. In particular, for Box-Jenkins models, a finite dimensional parametrization is provided which is able to generate all possible asymptotic covariance matrices. As a special case, the very common situation of a fixed controller during the identification experiment can be handled and optimal reference signal spectra can be computed subject to closed loop signal constraints. Finally, a brief numerical comparison with closed loop experiment design based on a high model order variance expression is presented.

  • 48.
    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.
    Finite model order accuracy in Hammerstein model estimation2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 10, p. 2640-2646Article in journal (Refereed)
    Abstract [en]

    Hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems. A static input nonlinearity followed by a linear dynamical part is an adequate way to model many real-life systems. This paper investigates the asymptotic (in terms of sample size) variance of Hammerstein model estimates. The work extends earlier results by Ninness and Gibson (2002) in the following ways. Not only frequency function estimation but estimation of general quantities is considered. The expressions are not restricted to be valid asymptotically in the model order. In addition, the results cover model structures having noise models and allow for data generated under feedback. The increase in variance due to the estimation of the input nonlinearity is characterized. In particular, under open loop operation, white additive noise and the assumption of a separable process, it is shown that the variance increase is exactly a term that was observed in Ninness and Gibson (2002) to result in good agreement with simulations. This term vanishes in the formal asymptotic in model order analysis in Ninness and Gibson (2002).

  • 49.
    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.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Söderström, Torsten
    Uppsala University.
    On the accuracy in errors-in-variables identification compared to prediction-error identification2011In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, ISSN 0005-1098, Vol. 47, no 12, p. 2704-2712Article in journal (Refereed)
    Abstract [en]

    Errors-in-variables estimation problems for single-inputsingle-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle's formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.

  • 50.
    Hjalmarsson, Håkan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Ninness, B.
    University of Newcastle.
    Least-squares estimation of a class of frequency functions: A finite sample variance expression2006In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 42, no 4, p. 589-600Article in journal (Refereed)
    Abstract [en]

    A new expression for the variance of scalar frequency functions estimated using the least-squares method is presented. The expression is valid for finite sample size and for a class of model structures, which includes finite impulse response, Laguerre and Kautz models, when the number of estimated parameters coincides with the number of excitation frequencies of the input. The expression gives direct insight into how excitation frequencies and amplitudes affect the accuracy of frequency function estimates. With the help of this expression, a severe sensitivity of the accuracy with respect to the excitation frequencies is exposed. The relevance of the expression when more excitation frequencies are used is also discussed.

1234 1 - 50 of 172
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