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  • 1.
    Abdalmoaty, Mohamed
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Hjalmarsson, Håkan
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Identification of Stochastic Nonlinear Models Using Optimal Estimating Functions2020Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 119, artikkel-id 109055Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The first part of the paper examines the asymptotic properties of linear prediction error method estimators, which were recently suggested for the identification of nonlinear stochastic dynamical models. It is shown that their accuracy depends not only on the shape of the unknown distribution of the data, but also on how the model is parameterized. Therefore, it is not obvious in general which linear prediction error method should be preferred. In the second part, the estimating functions approach is introduced and used to construct estimators that are asymptotically optimal with respect to a specific class of estimators. These estimators rely on a partial probabilistic parametric models, and therefore neither require the computations of the likelihood function nor any marginalization integrals. The convergence and consistency of the proposed estimators are established under standard regularity and identifiability assumptions akin to those of prediction error methods. The paper is concluded by several numerical simulation examples.

    Fulltekst (pdf)
    fulltext
  • 2.
    Abdalmoaty, Mohamed
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Hjalmarsson, Håkan
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Linear Prediction Error Methods for Stochastic Nonlinear Models2019Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, s. 49-63Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
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    fulltext
  • 3.
    Abolpour, Roozbeh
    et al.
    Shiraz Univ, Sch Elect & Comp Engn, Shiraz, Iran..
    Dehghani, Maryam
    Shiraz Univ, Sch Elect & Comp Engn, Shiraz, Iran..
    Hesamzadeh, Mohammad Reza
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Elektroteknik, Elkraftteknik.
    Inside-Ellipsoid Outside-Sphere (IEOS) model for general bilinear feasibility problems: Feasibility analysis and solution algorithm2023Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 147, s. 110738-, artikkel-id 110738Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper deals with general bilinear feasibility problems. A nonlinear transformation is introduced that reformulates a general bilinear feasibility problem as a Linear Matrix Inequality (LMI) problem augmented with a single non-convex quadratic constraint. The single non-convex quadratic constraint has a regular concave constraint function. Due to the LMI part of this formulation, it is easier to analyze, and we prove that the solution space of this formulation is located inside several ellipsoids and outside a sphere. This leads to our proposed Inside-Ellipsoid and Outside-Sphere (IEOS) model for general bilinear feasibility problems. Then, the feasibility analysis of our proposed IEOS model is performed. The related necessary feasibility conditions and sufficient feasibility conditions are theoretically developed. Moreover, an iterative algorithm for solving our IEOS model is also proposed.Two applications including matrix-factorization problem in control systems and power-flow prob-lem in power systems are considered to evaluate the practicality of our proposed approach. Both problems are formulated as IEOS models. It is shown that our proposed model can provide more accurate solutions to these problems as compared to previous competing approaches in the relevant literature.

  • 4.
    Agüero, Juan C.
    et al.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Goodwin, Graham C.
    The University of Newcastle, Australia.
    Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation2012Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, nr 4, s. 632-637Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 5.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Harmonic analysis of pulse-width modulated systems2009Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, nr 4, s. 851-862Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 6. Anderson, R. P.
    et al.
    Milutinović, D.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Self-triggered sampling for second-moment stability of state-feedback controlled SDE systems2015Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 54, s. 8-15Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 7. Aragues, Rosario
    et al.
    Shi, Guodong
    Dimarogonas, Dimos V.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Saguees, Carlos
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Mezouar, Youcef
    Distributed algebraic connectivity estimation for undirected graphs with upper and lower bounds2014Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, nr 12, s. 3253-3259Artikkel i tidsskrift (Fagfellevurdert)
    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).

  • 8.
    Barenthin, Märta
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Bombois, Xavier
    TU Delft.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Scorletti, Gerard
    Ecole Centrale de Lyon.
    Identification for control of multivariable systems: Controller validation and experiment design via LMIs2008Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, nr 12, s. 3070-3078Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 9.
    Barenthin, Märta
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Identification and control: Joint input design and H-infinity state feedback with ellipsoidal parametric uncertainty via LMIs2008Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, nr 2, s. 543-551Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 10.
    Beerens, R.
    et al.
    Eindhoven Univ Technol, Dept Mech Engn, NL-5600 MB Eindhoven, Netherlands..
    Bisoffi, Andrea
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    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 friction2019Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 107, s. 483-492Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 11.
    Berkane, Soulaimaine
    et al.
    Department of Computer Science and Engineering, University of Quebec in Outaouais, 101 St-Jean Bosco, Gatineau, QC, J8X 3X7, Canada.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Constrained stabilization on the n-sphere2021Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 125, artikkel-id 109416Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We solve the stabilization problem on the n-sphere in the presence of conic constraints. We use the stereographic projection to map this problem to the classical navigation problem on Rn in the presence of spherical obstacles. As a consequence, any obstacle avoidance algorithm for navigation in the Euclidean space can be used to solve the given problem on the n-sphere. We illustrate the effectiveness of the approach using the kinematics of the reduced attitude model on the 2-sphere. 

  • 12.
    Berkane, Soulaimane
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Tayebi, A.
    Attitude estimation with intermittent measurements2019Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, s. 415-421Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 13.
    Bishop, Adrian N.
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS. KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Fidan, Baris
    Anderson, Brian D. O.
    Dogancay, Kutluyil
    Pathirana, Pubudu N.
    Optimality analysis of sensor-target localization geometries2010Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, nr 3, s. 479-492Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 14.
    Bisoffi, Andrea
    et al.
    Univ Trento, Dipartimento Ingn Ind, Trento, Italy..
    Bergsåker, Henric
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Bykov, Igor
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Elevant, Thomas
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Frassinetti, Lorenzo
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Garcia Carrasco, Alvaro
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Hellsten, Torbjörn
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Ivanova, Darya
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Jonsson, Thomas
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Menmuir, Sheena
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Petersson, Per
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Rachlew, Elisabeth
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Atom- och molekylfysik.
    Rubel, Marek
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Ström, Petter
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Tholerus, Simon
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Weckmann, Armin
    KTH, Skolan för elektro- och systemteknik (EES), Fusionsplasmafysik.
    Zychor, I.
    Inst Plasma Phys & Laser Microfus, PL-01497 Warsaw, Poland..
    et al.,
    Hybrid cancellation of ripple disturbances arising in AC/DC converters2017Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 77, s. 344-352Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In AC/DC converters, a peculiar periodic nonsmooth waveform arises, the so-called ripple. In this paper we propose a novel model that captures this nonsmoothness by means of a hybrid dynamical system performing state jumps at certain switching instants, and we illustrate its properties with reference to a three phase diode bridge rectifier. As the ripple corrupts an underlying desirable signal, we propound two observer schemes ensuring asymptotic estimation of the ripple, the first with and the second without knowledge of the switching instants. Our theoretical developments are well placed in the context of recent techniques for hybrid regulation and constitute a contribution especially for our second observer, where the switching instants are estimated. Once asymptotic estimation of the ripple is achieved, the ripple can be conveniently canceled from the desirable signal, and thanks to the inherent robustness properties of the proposed hybrid formulation, the two observer schemes require only that the desirable signal is slowly time varying compared to the ripple. Exploiting this fact, we illustrate the effectiveness of our second hybrid observation law on experimental data collected from the Joint European Torus tokamak.

  • 15. Boem, F.
    et al.
    Zhou, Y.
    Fischione, Carlo
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Parisini, T.
    Distributed Pareto-optimal state estimation using sensor networks2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 93, s. 211-223Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 16.
    Bombois, Xavier
    et al.
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, Ecully, France.;CNRS, Paris, France..
    Colin, Kevin
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Van den Hof, Paul M. J.
    Eindhoven Univ Technol, Control Syst Grp, Dept Elect Engn, Eindhoven, Netherlands..
    Hjalmarsson, Håkan
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    On the informativity of direct identification experiments in dynamical networks2023Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 148, s. 110742-, artikkel-id 110742Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Data informativity is a crucial property to ensure the consistency of the prediction error estimate. This property has thus been extensively studied in the open-loop and in the closed-loop cases, but has only been briefly touched upon in the dynamic network case. In this paper, we consider the prediction error identification of the modules in a row of a dynamic network using the full input approach. Our main contribution is to propose a number of easily verifiable data informativity conditions for this identification problem. Among these conditions, we distinguish a sufficient data informativity condition that can be verified based on the topology of the network and a necessary and sufficient data informativity condition that can be verified via a rank condition on a matrix of coefficients that are related to a full-order model structure of the network. These data informativity conditions allow to determine different situations (i.e., different excitation patterns) leading to data informativity. In order to be able to distinguish between these different situations, we also propose an optimal experiment design problem that allows to determine the excitation pattern yielding a certain pre-specified accuracy with the least excitation power.

  • 17.
    Bombois, Xavier
    et al.
    TU Delft.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Scorletti, Gerard
    Ecole Centrale de Lyon.
    Identification for robust H-2 deconvolution filtering2010Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, nr 3, s. 577-584Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 18. Bombois, Xavier
    et al.
    Korniienko, A.
    Hjalmarsson, Håkan
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Scorletti, G.
    Optimal identification experiment design for the interconnection of locally controlled systems2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, s. 169-179Artikkel i tidsskrift (Fagfellevurdert)
    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. 

    Fulltekst (pdf)
    fulltext
  • 19.
    Bombois, Xavier
    et al.
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, 36 Ave Guy Collongue, Ecully, France.;Ctr Natl Rech Sci CNRS, Paris, France..
    Morelli, Federico
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, 36 Ave Guy Collongue, Ecully, France..
    Hjalmarsson, Håkan
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Bako, Laurent
    Univ Lyon, Lab Ampere, Ecole Cent Lyon, 36 Ave Guy Collongue, Ecully, France..
    Colin, Kevin
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Robust optimal identification experiment design for multisine excitation2021Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 125, artikkel-id 109431Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal.

  • 20.
    Boskos, Dimitris
    et al.
    Univ Calif San Diego, Dept Mech & Aerosp Engn, San Diego, CA 92103 USA..
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Finite horizon discrete models for multi-agent control systems with coupled dynamics2020Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 115, artikkel-id 108838Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The goal of this paper is to obtain online abstractions for coupled multi-agent systems in a decentralized manner. A discrete model which captures the motion capabilities of each agent is derived over a bounded time-horizon, by discretizing a corresponding overapproximation of the agent's reachable states. The individual abstractions' composition provides a correct representation of the coupled continuous system over the horizon and renders the approach appropriate for control synthesis under high-level specifications which are assigned to the agents over this time window. Sufficient conditions are also provided for the space and time discretization to guarantee the derivation of deterministic abstractions with tunable transition capabilities.

  • 21.
    Bottegal, Giulio
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Aravkin, Aleksandr Y.
    Hjalmarsson, Hakan
    Pillonetto, Gianluigi
    Robust EM kernel-based methods for linear system identification2016Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 67, s. 114-126Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 22.
    Bottegal, Giulio
    et al.
    Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Pillonetto, Gianluigi
    Department of Information Engineering, University of Padova, Padova, Italy.
    A new kernel-based approach to system identification with quantized output data2017Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 85, s. 145-152Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 23. Cantoni, M.
    et al.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Computing the L-2 gain for linear periodic continuous-time systems2009Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, nr 3, s. 783-789Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 24. Carli, Ruggero
    et al.
    Fagnani, Fabio
    Speranzon, Alberto
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Zampieri, Sandro
    Communication constraints in the average consensus problem2008Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, nr 3, s. 671-684Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 25.
    Carvalho, J. Frederico
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Robotik, perception och lärande, RPL. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Pequito, S.
    Aguiar, A. P.
    Kar, S.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Composability and controllability of structural linear time-invariant systems: Distributed verification2017Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 78, s. 123-134Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 26.
    Chen, Fei
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    On topological conditions for enabling transient control in leader–follower networks2024Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 166, artikkel-id 111693Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive necessary and sufficient conditions for leader–follower multi-agent systems such that we can further apply prescribed performance control to achieve the desired formation while satisfying certain transient constraints. A leader–follower framework is considered in the sense that a group of agents with external inputs are selected as leaders in order to drive the group of followers in a way that the entire system can achieve target formation within certain prescribed performance transient bounds. We first derive necessary conditions on the leader–follower graph topology under which the target formation together with the prescribed performance guarantees can be fulfilled. Afterwards, the derived necessary conditions are extended to necessary and sufficient conditions for leader–follower formation control under transient constraints. Finally, the proposed results are illustrated with simulation examples.

  • 27.
    Cortez, Wenceslao Shaw
    et al.
    Pacific Northwest Natl Lab, Richland, WA 99354 USA..
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Safe-by-design control for Euler-Lagrange systems2022Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 146, s. 110620-, artikkel-id 110620Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Safety-critical control is characterized as ensuring constraint satisfaction for a given dynamical system. Recent developments in zeroing control barrier functions (ZCBFs) have provided a framework for ensuring safety of a superlevel set of a single constraint function. Euler-Lagrange systems represent many real-world systems including robots and vehicles, which must abide by safety-regulations, especially for use in human-occupied environments. These safety regulations include state constraints (position and velocity) and input constraints that must be respected at all times. ZCBFs are valuable for satisfying system constraints for general nonlinear systems, however their construction to satisfy state and input constraints is not straightforward. Furthermore, the existing barrier function methods do not address the multiple state constraints that are required for safety of Euler-Lagrange systems. In this paper, we propose a methodology to construct multiple, non-conflicting control barrier functions for Euler-Lagrange systems subject to input constraints to satisfy safety regulations, while concurrently taking into account robustness margins and sampling-time effects. The proposed approach consists of a sampled-data controller and an algorithm for barrier function construction to enforce safety (i.e. satisfy position and velocity constraints). The proposed method is validated in simulation on a 2-DOF planar manipulator.

  • 28. Dai, L.
    et al.
    Gao, Yulong
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Xie, L.
    Johansson, Karl Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Xia, Y.
    Stochastic self-triggered model predictive control for linear systems with probabilistic constraints2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 92, s. 9-17Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 29. Delellis, P.
    et al.
    Di Bernardo, M.
    Liuzza, Davide
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, 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 systems2015Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 56, s. 1-11Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 30.
    Della Rossa, Matteo
    et al.
    UCLouvain, ICTEAM, Louvain La Neuve, Belgium..
    Pasquini, Mirko
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. AdBIOPRO, Competence Ctr Adv Bioprod Continuous Proc, Stockholm, Sweden..
    Angeli, David
    Imperial Coll, Dept Elect & Elect Engn, London, England.;Univ Florence, Dip Ingn Informaz, Florence, Italy..
    Continuous-time switched systems with switching frequency constraints: Path-complete stability criteria2022Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 137, s. 110099-, artikkel-id 110099Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose a novel Lyapunov construction for continuous-time switched systems relying on a graph theoretical Lyapunov construction. Starting with a finite family of continuously differentiable functions, suitable inequalities involving these functions and the vector fields defining the switched system are encoded in a direct and labeled graph. We then provide sufficient conditions for (asymptotic) stability subject to constrained switching times, by relying on the path-completeness of the chosen graph. The analysis is first carried out under the hypothesis of constant switching frequency. Then, the results are generalized to dwell time setting. In the case of linear dynamics, the graph formalism allows us to interpret the existing results on dwell time stability in a unified language. Some numerical examples illustrate the usefulness of the conditions.

  • 31.
    Dimarogonas, Dimos V.
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control2010Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 46, nr 4, s. 695-700Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    multiagent_automatica10
  • 32.
    Dimarogonas, Dimos V.
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Kyriakopoulos, K. J.
    A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems2008Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, nr 10, s. 2648-2654Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 33. Duerr, Hans-Bernd
    et al.
    Stankovic, Milos S.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Ebenbauer, Christian
    Extremum seeking on submanifolds in the Euclidian space2014Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, nr 10, s. 2591-2596Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 34. Dürr, Hans-Bernd
    et al.
    Stankovic, Milos S.
    Ebenbauer, Christian
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Lie bracket approximation of extremum seeking systems2013Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, nr 6, s. 1538-1552Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 35. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Cost function shaping of the output error criterion2017Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 76, s. 53-60Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 36. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Input design as a tool to improve the convergence of PEM2013Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, nr 11, s. 3282-3291Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 37. Esparza, Alicia
    et al.
    Agüero, Juan C.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Godoy, Boris I.
    The University of Newcastle, Australia.
    Asymptotic statistical analysis for model-based control design strategies2011Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, nr 5, s. 1041-1046Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 38.
    Everitt, Niklas
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    Eindhoven Univ Technol, Dept Elect Engn, Eindhoven, Netherlands..
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    An empirical Bayes approach to identification of modules in dynamic networks2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 91, s. 144-151Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 39.
    Everitt, Niklas
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Galrinho, Miguel
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method2018Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, s. 221-234Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 40.
    Fanizza, Giovanna
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Nagamune, Ryozo
    Univ British Columbia, Dept Mech Engn.
    Spectral estimation by least-squares optimization based on rational covariance extension2007Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, nr 2, s. 362-370Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 41.
    Farokhi, Farhad
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, 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, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems2013Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, nr 2, s. 326-337Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 42.
    Farokhi, Farhad
    et al.
    CSIROs Data61, Canberra, ACT, Australia.; Univ Melbourne, Dept Elect & Elect Engn, Melbourne, Vic, Australia..
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Ensuring privacy with constrained additive noise by minimizing Fisher information2019Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 99, s. 275-288Artikkel i tidsskrift (Fagfellevurdert)
    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

  • 43. Farokhi, Farhad
    et al.
    Shames, Iman
    Rabbat, Michael G.
    Johansson, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    On reconstructability of quadratic utility functions from the iterations in gradient methods2016Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 66, s. 254-261Artikkel i tidsskrift (Fagfellevurdert)
    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. 

  • 44.
    Fotiadis, Filippos
    et al.
    School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA.
    Kanellopoulos, Aris
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Teknisk informationsvetenskap.
    Vamvoudakis, Kyriakos G.
    School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA.
    Hugues, Jerome
    Carnegie Mellon University/Software Engineering Institute, Pittsburgh, PA, USA.
    On the effect of clock offsets and quantization on learning-based adversarial games2024Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 167, artikkel-id 111762Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work, we consider systems whose components suffer from clock offsets and quantization and study the effect of those on a reinforcement learning (RL) algorithm. Specifically, we consider an off-policy iterative RL algorithm for continuous-time systems, which uses input and state data to approximate the Nash-equilibrium of a zero-sum game. However, the data used by this algorithm are not consistent with one another, in that each of them originates from a slightly different time instant of the past, hence putting the convergence of the algorithm in question. We prove that, given that these timing inconsistencies remain below a certain threshold, the iterative off-policy RL algorithm will still converge epsilon-closely to the desired Nash policy. However, this result is conditional to a certain Lipschitz continuity and differentiability condition on the input-state data collected, which is indispensable in the presence of clock offsets. A similar result is also derived when quantization of the measured state is considered. Finally, unlike prior work, we provide a sufficiently rich data condition for the execution of the iterative RL algorithm, which can be verified a priori across all iteration indices. Simulations are performed, which verify and clarify theoretical findings.

  • 45. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    LQ optimal control for a class of pulse width modulated systems2007Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, nr 6, s. 1009-1020Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 46. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Robust tracking with H-infinity performance for PWM systems2009Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, nr 8, s. 1808-1818Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 47.
    Galrinho, Miguel
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Rojas, Cristián R.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Hjalmarsson, Håkan
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Estimating models with high-order noise dynamics using semi-parametric weighted null-space fitting2019Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 102, s. 45-57Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 48.
    Gao, Yulong
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Cannon, Mark
    Univ Oxford, Dept Engn Sci, Oxford OX1 3PJ, England..
    Xie, Lihua
    Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore..
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH Royal Inst Technol, Sch Elect Engn & Comp Sci, SE-10044 Stockholm, Sweden..
    Invariant cover: Existence, cardinality bounds, and computation2021Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 129, artikkel-id 109588Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An invariant cover quantifies the information needed by a controller to enforce an invariance specification. This paper investigates some fundamental problems concerning existence and computation of an invariant cover for uncertain discrete-time linear control systems subject to state and control constraints. We develop necessary and sufficient conditions on the existence of an invariant cover for a polytopic set of states. The conditions can be checked by solving a set of linear programs, one for each extreme point of the state set. Based on these conditions, we give upper and lower bounds on the minimal cardinality of the invariant cover, and design an iterative algorithm with finite-time convergence to compute an invariant cover. We further show in two examples how to use an invariant cover in the design of a coder-controller pair that ensures invariance of a given set for a networked control system with a finite communication data rate.

  • 49.
    Gao, Yulong
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Yu, Pian
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    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 analysis2019Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 107, s. 574-581Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 50.
    Gerencser, Laszlo
    et al.
    Computer and Automation Institute of the Hungarian Academy of Sciences, (MTA SZTAKI),.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Mårtensson, Jonas
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design2009Inngår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, nr 3, s. 623-633Artikkel i tidsskrift (Fagfellevurdert)
    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.

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