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  • 1.
    Atta, Khalid
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Guay, Martin
    Department of Chemical Engineering, Queen’s University, Kingston, ON, Canada.
    Comment on “On stability and application of extremum seeking control without steady-state oscillation” [Automatica 68 (2016) 18–26]2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 103, p. 580-581Article in journal (Refereed)
    Abstract [en]

    This correspondence revisits the results reported in a recent Automatica paper (Wang et al., 2016). We show that the claim of exponential stability of the extremum-seeking control system presented in Theorem 1 is not correct. An alternative stability analysis using the Lyapunov–Malkin theorem is considered. A counterexample is also presented.

  • 2.
    Gustafsson, T.K.
    et al.
    Åbo Akademi University, Department of Engineering.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Modelling of uncertain systems via linear programming1996In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 32, no 3, p. 319-335Article in journal (Refereed)
    Abstract [en]

    Real plants are, in general, time-varying and uncertain. Yet most industrial control loops are designed using linear time-invariant (LTI) plant models. The present work formalizes the problem of best approximate LTI modelling of BIBO-stable linear time-varying (LTV) systems in a way that is compatible with the notion of induced l∞ norm used in robust l1 control. This setup is closely associated with certain identification methods and controlmotivated model validation/invalidation procedures that can be efficiently implemented with special-purpose linear programming (LP) techniques. Results are given for approximate modelling of BIBO-stable LTV and LTI systems using LTI models, especially BIBO-stable fixed-pole state-space model parametrizations. It is shown that such parametrizations are satisfactory from an approximate modelling point of view, and can be used in output-error-type LP identification techniques and in LP model validation procedures. Various useful constraints on model parameters etc. can be included, as long as they are linear in the unknown parameters, and both insensitive (statistically robust) and sensitive criteria can be used in identification and model validation. Simulation examples are included to illustrate that such techniques indeed give good results and can be used to solve problems of realistic size.

  • 3.
    Johansson, Andreas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Bask, Michael
    Norlander, Torbjörn
    Dynamic threshold generators for robust fault detection in linear systems with parameter uncertainty2006In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 42, no 7, p. 1095-1106Article in journal (Refereed)
    Abstract [en]

    The problem of developing robust thresholds for fault detection is addressed. An inequality for the solution of a linear system with uncertain parameters is provided and is shown to be a valuable tool for developing dynamic threshold generators for fault detection. Such threshold generators are desirable for achieving robustness against model uncertainty in combination with sensitivity to small faults. The usefulness of the inequality is illustrated by developing an algorithm for detection of sensor faults in a turbofan engine. The proposed algorithm consists of a state observer with integral action. A dynamic threshold generator is derived under the assumption of parametric uncertainty in the process model. Successful simulations with measurement data show that the algorithm is capable of detecting faults without generating false alarms.

  • 4.
    Johansson, Andreas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Medvedev, Alexander
    An observer for systems with nonlinear output map2003In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 39, no 5, p. 909-918Article in journal (Refereed)
    Abstract [en]

    A nonlinear observer, with the feedback gain weighted by the sensitivity of the output with respect to the state, is developed for systems with nonlinear output map. The observer can be obtained from the extended Kalman filter by a special choice of time-varying weighting matrices. It is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived. The observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal. Using plant data from the converter at SSAB Oxelösund AB, the observer is shown to provide accurate estimates of the carbon content.

  • 5.
    Medvedev, Alexander
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Disturbance attenuation in finite spectrum assignment controllers1997In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 33, no 6, p. 1163-1168Article in journal (Refereed)
    Abstract [en]

    Two finite-spectrum-assignment controllers for continuous linear dynamic systems with multiple time delays in input signal are introduced. The controllers are shown to comprise least-squares state estimators. Disturbance attenuation properties stipulated by the choice of shift operator in the observers are studied.

  • 6.
    Medvedev, Alexander
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Fault detection and isolation by a continuous parity space method1995In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 31, no 7, p. 1039-1044Article in journal (Refereed)
    Abstract [en]

    The well-known parity space method for fault detection and isolation is generalized to a continuous-time case. As in the discrete-time case, it is shown that the parity space equations can be implemented using a number of time delays, and are equivalent to a continuous deadbeat observer. Algorithms for isolation of sensor and actuator faults are derived and illustrated by a numerical example. (

  • 7.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J. R.
    School of Mathematics, University of Leeds.
    Gustafsson, T.K.
    Faculty of Chemical Engineering, Åbo Akademi.
    Worst-case control-relevant identification1995In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 31, no 12, p. 1799-1819Article in journal (Refereed)
    Abstract [en]

    This paper introduces the reader to several recent developments in worst-case identification motivated by various issues of modelling of systems from data for the purpose of robust control design. Many aspects of identification in H∞ and ℓ1 are covered including algorithms, convergence and divergence results, worst-case estimation of uncertainty models, model validation and control relevancy issues.

  • 8.
    Partington, J.R.
    et al.
    School of Mathematics, University of Leeds.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Analysis of linear methods for robust identification in l11995In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 31, no 5, p. 755-758Article in journal (Refereed)
    Abstract [en]

    We consider worst-case analysis of system identification by means of the linear algorithms such as least-squares. We provide estimates for worst-case and average errors, showing that worst-case robust convergence cannot occur in the l1 identification problem. The case of periodic inputs is also analysed. Finally a pseudorandomness assumption is introduced that allows more powerful convergence results in a deterministic framework.

  • 9.
    Sayyaddelshad, Saleh
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Johansson, Andreas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Darouach, Mohamed
    Université de Lorraine, CRAN-CNRS UMR 7039, IUT de Longwy, 186 Rue de Lorraine.
    Gustafsson, Thomas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Robust state estimation and unknown inputs reconstruction for a class of nonlinear systems: multiobjective approach2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 64, p. 1-7Article in journal (Refereed)
    Abstract [en]

    We consider a novel method to design H-infinity observers for a class of uncertain nonlinear systems subject to unknown inputs. First, the main system dynamics are rewritten as an augmented system with state vector including both the state vector of the main system and the unknown inputs. Then, we design a H-infinity reduced-order observer to estimate both state variables and unknown inputs simultaneously. Based on a Lyapunov functional, we derive a sufficient condition for existence of the designed observer which requires solving a nonlinear matrix inequality. To facilitate the observer design, the achieved condition is formulated in terms of a set of linear matrix inequalities (LMI). By extending the proposed method to a multiobjective optimization problem, the maximum bound of the uncertainty and the minimum value of the disturbance attenuation level are found. Finally, the proposed observer is illustrated with an example.

  • 10.
    Toivonen, Hannu T.
    et al.
    Department of Chemical Engineering, Åbo Akademi.
    Medvedev, Alexander
    Damping of harmonic disturbances in sampled-data systems: parameterization of all optimal controllers2003In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 39, no 1, p. 75-80Article in journal (Refereed)
    Abstract [en]

    Optimal damping of harmonic disturbances of known frequencies is studied for sampled-data systems. A sampled-data output feedback controller is designed to minimize the intersample variations of the controlled variable. The set of all stabilizing optimal controllers is obtained in terms of the Youla parameterization and a set of interpolation conditions at the disturbance frequencies, which ensure that the stationary cost is minimized.

  • 11.
    Wahlberg, B.
    et al.
    S3 — Automatic Control, Royal Institute of Technology.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    On approximation of stable linear dynamical systems using Laguerre and Kautz functions1996In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 32, no 5, p. 693-708Article in journal (Refereed)
    Abstract [en]

    Approximation of stable linear dynamical systems by means of so-called Laguerre and Kautz functions, which are the Laplace transforms of a class of orthonormal exponentials, is studied. Since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials (times polynomials), it seems reasonable to use basis functions of the same type. Assuming that the transfer function of a system is bounded and analytic outside a given disc, it is shown that Laguerre basis functions are optimal in a mini-max sense. This result is extended to the "two-parameter" Kautz functions which can have complex poles, while the poles of Laguerre functions are restricted to the real axis. By conformal mapping techniques the "two-parameter" Kautz approximation problem is recast as two Laguerre approximation problems. Thus, the well-developed theory of Laguerre functions can be applied to analyze Kautz approximations. Unilateral shifts are used to further develop the connection between Laguerre functions and Kautz functions. Results on H2 and H∞ approximation using Kautz models are given. Furthermore, the weighted L2 Kautz approximation problem is shown to be equivalent to solving a block Toeplitz matrix equation

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