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Yoshio Ebihara - One of the best experts on this subject based on the ideXlab platform.

  • on gain scheduled state feedback Controller Synthesis with quadratic stability condition
    IEEE Control Systems Letters, 2020
    Co-Authors: Yoshio Ebihara, Noboru Sebe, Hayato Waki
    Abstract:

    This letter shows that, as long as continuous-time linear parameter-varying (LPV) systems are concerned, quadratic-stability-based gain-scheduled state-feedback Controller Synthesis offers no advantage over quadratic-stability-based fixed (parameter-independent) state-feedback Controller Synthesis in typical control performance specifications. We derive this counterintuitive result by properly extending the previous results on the robust versions of Finsler’s lemma and the elimination lemma. We also show that this counterintuitive result is continuous-time LPV system specific, and in the discrete-time LPV system case quadratic-stability-based gain-scheduled state-feedback Controller Synthesis does bring improvement. These results give a proper warning about the effectiveness of the quadratic-stability-based gain-scheduled state-feedback Controller Synthesis.

  • Robust Controller Synthesis of Periodic Discrete-Time Systems
    S-Variable Approach to LMI-Based Robust Control, 2014
    Co-Authors: Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Abstract:

    Finally, Chapter 8 deals with state-feedback Controller Synthesis for discrete-time periodic systems. By introducing S-variables and applying change of variables that is almost identical to the LTI case, we can readily obtain SV-LMIs for periodic state-feedback Controller Synthesis. We illustrate by numerical examples that the SV-LMIs are indeed effective in conservatism reduction when dealing with discrete-time periodic systems affected by polytopic uncertainties.

  • periodically time varying memory state feedback Controller Synthesis for discrete time linear systems
    Automatica, 2011
    Co-Authors: Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Abstract:

    In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback Controller Synthesis. In stark contrast with existing approaches that are confined to memoryless static Controller Synthesis, we explore dynamical Controller Synthesis and reveal a particular periodically time-varying memory state-feedback Controller (PTVMSFC) structure that allows LMI-based Synthesis. In the context of robust Controller Synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static Controller Synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is "exact" in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.

  • LMI-based Periodically Time-Varying Dynamical Controller Synthesis for Discrete-Time Uncertain Linear Systems
    IFAC Proceedings Volumes, 2008
    Co-Authors: Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Abstract:

    Abstract In this paper, we propose a new LMI-based method for robust state-feedback Controller Synthesis of discrete-time linear periodic/time-invariant systems subject to polytopic uncertainties. In stark contrast with existing approaches that are confined to static Controller Synthesis, we explore dynamic Controller Synthesis and reveal a particular periodically time-varying dynamical Controller structure that allows LMI-based Synthesis. In particular, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective to achieve less conservative results.

Jinjin Liu - One of the best experts on this subject based on the ideXlab platform.

  • Controller Synthesis for switched positive linear systems by output feedback
    International Journal of Systems Science, 2018
    Co-Authors: Jinjin Liu
    Abstract:

    The output-feedback Controller Synthesis issue for a class of continuous-time switched linear systems via average dwell time switching with constrained controls and output is addressed. First, we f...

  • Controller Synthesis for switched positive linear systems
    2014 International Conference on Information Science Electronics and Electrical Engineering, 2014
    Co-Authors: Jinjin Liu, Kanjian Zhang, Haikun Wei
    Abstract:

    This paper addresses the Controller Synthesis for a class of continuous-time switched positive linear systems. A sufficient condition for the existence of a set of state-feedback Controllers which guarantee the positivity and stability of the closed-loop systems for switched positive linear systems are presented, including the requirement of positive or negative Controllers. In addition, the Controller Synthesis problems with interval and polytopic uncertainties are also addressed. All the obtained conditions are solved in terms of Linear Programming. Finally, numerical examples are provided to illustrate the effectiveness of the result.

Antoine Girard - One of the best experts on this subject based on the ideXlab platform.

  • Lazy Safety Controller Synthesis with Multi-Scale Adaptive-Sampling Abstractions of Nonlinear Systems
    2020
    Co-Authors: Elena Ivanova, Antoine Girard
    Abstract:

    In this paper, we present an abstraction-based approach to safety Controller Synthesis for continuous-time nonlinear systems. To reduce the computational burden associated with symbolic control approaches, we develop a lazy Controller Synthesis algorithm, which uses the incremental forward exploration of the symbolic dynamics, allowing us to restrict the Controller Synthesis computations to reachable states only. We propose using this algorithm with novel multi-scale abstractions, which also use adaptive time sampling. Transition duration is constrained by intervals that must contain the reachable set, which enables a better control of the symbolic transitions as opposed to using transitions of predetermined duration. Implementation of the algorithm and Controller refinement are discussed. We provide a simple example to illustrate this benefits of the approach.

  • Controller Synthesis for safety and reachability via approximate bisimulation
    Automatica, 2012
    Co-Authors: Antoine Girard
    Abstract:

    In this paper, we consider the problem of Controller design using approximately bisimilar abstractions with an emphasis on safety and reachability specifications. We propose abstraction-based approaches to Controller Synthesis for both types of specifications. We start by synthesizing a Controller for an approximately bisimilar abstraction. Then, using a concretization procedure, we obtain a Controller for our initial system that is proved "correct by design". We provide guarantees of performance by giving estimates of the distance of the synthesized Controller to the maximal (i.e., the most permissive) safety Controller or to the time-optimal reachability Controller. Finally, we use these techniques, combined with discrete approximately bisimilar abstractions of switched systems developed recently, for switching Controller Synthesis.

  • Brief paper: Controller Synthesis for safety and reachability via approximate bisimulation
    Automatica, 2012
    Co-Authors: Antoine Girard
    Abstract:

    In this paper, we consider the problem of Controller design using approximately bisimilar abstractions with an emphasis on safety and reachability specifications. We propose abstraction-based approaches to Controller Synthesis for both types of specifications. We start by synthesizing a Controller for an approximately bisimilar abstraction. Then, using a concretization procedure, we obtain a Controller for our initial system that is proved ''correct by design''. We provide guarantees of performance by giving estimates of the distance of the synthesized Controller to the maximal (i.e., the most permissive) safety Controller or to the time-optimal reachability Controller. Finally, we use these techniques, combined with discrete approximately bisimilar abstractions of switched systems developed recently, for switching Controller Synthesis.

Tomomichi Hagiwara - One of the best experts on this subject based on the ideXlab platform.

  • Kernel Approximation Approach to the L 1 Optimal Sampled-Data Controller Synthesis Problem
    IFAC-PapersOnLine, 2017
    Co-Authors: Tomomichi Hagiwara
    Abstract:

    Abstract This paper is concerned with a new framework called the kernel approximation approach to the L1 optimal Controller Synthesis problem of sampled-data systems. On the basis of the lifted representation of sampled-data systems, which contains an input operator and an output operator, this paper introduces a method for approximating the kernel function of the input operator and the hold function of the output operator by piecewise constant functions. Through such a method, the L1 optimal sampled-data Controller Synthesis problem could be (almost) equivalently converted into the discrete-time l1 optimal Controller Synthesis problem. This paper further establishes an important inequality that forms the theoretical validity of the kernel approximation approach for tackling the L1 optimal sampled-data Controller Synthesis problem.

  • Kernel Approximation Approach to the L1 Optimal Sampled-Data Controller Synthesis Problem
    IFAC-PapersOnLine, 2017
    Co-Authors: Jung Hoon Kim, Tomomichi Hagiwara
    Abstract:

    Abstract This paper is concerned with a new framework called the kernel approximation approach to the L1 optimal Controller Synthesis problem of sampled-data systems. On the basis of the lifted representation of sampled-data systems, which contains an input operator and an output operator, this paper introduces a method for approximating the kernel function of the input operator and the hold function of the output operator by piecewise constant functions. Through such a method, the L1 optimal sampled-data Controller Synthesis problem could be (almost) equivalently converted into the discrete-time l1 optimal Controller Synthesis problem. This paper further establishes an important inequality that forms the theoretical validity of the kernel approximation approach for tackling the L1 optimal sampled-data Controller Synthesis problem.

  • $L_{1}$ Discretization for Sampled-Data Controller Synthesis via Piecewise Linear Approximation
    IEEE Transactions on Automatic Control, 2016
    Co-Authors: Jung Hoon Kim, Tomomichi Hagiwara
    Abstract:

    This paper develops a new discretization method with piecewise linear approximation for the $L_{1}$ optimal Controller Synthesis problem of sampled-data systems, which is the problem of minimizing the $L_{\infty}$ -induced norm of sampled-data systems. We apply fast-lifting on the top of the lifting technique, by which the sampling interval $[0,h)$ is divided into $M$ subintervals with an equal width. The signals on each subinterval are then approximated by linear functions by introducing two types of ‘linearizing operators’ for input and output, which leads to piecewise linear approximation of sampled-data systems. By using the arguments of preadjoint operators, we provide an important inequality that forms a theoretical basis for tackling the $L_{1}$ optimal Controller Synthesis problem of sampled-data systems more efficiently than the conventional method. More precisely, a mathematical basis for the piecewise linear approximation method associated with the convergence rate is shown through this inequality, and this suggests that the piecewise linear approximation method may drastically outperform the conventional method in the $L_{1}$ optimal Controller Synthesis problem of sampled-data systems. We then provide a discretization procedure of sampled-data systems by which the $L_{1}$ optimal Controller Synthesis problem is converted to the discrete-time $l_{1}$ optimal Controller Synthesis problem. Finally, effectiveness of the proposed method is demonstrated through a numerical example.

Dennis S. Bernstein - One of the best experts on this subject based on the ideXlab platform.

  • Stable ?2-optimal Controller Synthesis
    Optimal Control Applications and Methods, 2000
    Co-Authors: Joseph R. Corrado, R. Scott Erwin, Dennis S. Bernstein, Wassim M. Haddad
    Abstract:

    This paper considers fixed-structure stable ℋ2-optimal Controller Synthesis using a multiobjective optimization technique which provides a trade-off between closed-loop performance and the degree of Controller stability. The problem is presented in a decentralized static output feedback framework developed for fixed-structure dynamic Controller Synthesis. A quasi-Newton/continuation algorithm is used to compute solutions to the necessary conditions. To demonstrate the approach, two numerical examples are considered. The first example is a second-order spring–mass–damper system and the second example is a fourth-order two-mass system, both of which are considered in the stable stabilization literature. The results are then compared with other methods of stable compensator Synthesis. Copyright © 2000 John Wiley & Sons, Ltd.

  • Robust fixed-structure Controller Synthesis using the implicit small-gain bound
    Journal of the Franklin Institute, 2000
    Co-Authors: Wassim M. Haddad, Joseph R. Corrado, Vijaysekhar Chellaboina, Dennis S. Bernstein
    Abstract:

    Abstract In this paper we explore the applicability of the implicit small-gain guaranteed cost bound for Controller Synthesis. For flexibility in Controller Synthesis, we adopt the approach of fixed-structure Controller design which allows consideration of arbitrary Controller structures, including order, internal structure, and decentralization. A numerical example that has been addressed in the literature by means of alternative guaranteed cost bounds is presented to demonstrate the fixed-structure/implicit small-gain approach to robust Controller Synthesis.

  • Stable 7&-Opt imal Controller Synthesis
    1997
    Co-Authors: Joseph R. Corrade, R. Scott Erwin, Dennis S. Bernstein, Wassim M. Haddadl
    Abstract:

    This paper considers fixed-structure stable '&-optimal Controller Synthesis using a multiobjective optimization technique. The problem is presented in a decentralized static output feedback framework developed for fixed-structure dynamic Controller Synthesis. A quasi-Newton/continuation algorithm is used to compute solutions to the necessary conditions. To demonstrate the approach, a numerical example is considered, which consists of a second-order spring-mass-damper system pulled from the stable stabilization literature. The results are then compared with other methods of stable compensator Synthesis.

  • Stable H/sub 2/-optimal Controller Synthesis
    Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997
    Co-Authors: Joseph R. Corrado, R. Scott Erwin, Dennis S. Bernstein, Wassim M. Haddad
    Abstract:

    This paper considers fixed-structure stable H/sub 2/-optimal Controller Synthesis using a multiobjective optimization technique. The problem is presented in a decentralized static output feedback framework developed for fixed-structure dynamic Controller Synthesis. A quasi-Newton/continuation algorithm is used to compute solutions to the necessary conditions. To demonstrate the approach, a numerical example is considered, which consists of a second-order spring-mass-damper system pulled from the stable stabilization literature. The results are then compared with other methods of stable compensator Synthesis.

  • Robust fixed-structure Controller Synthesis using the implicit small gain bound
    Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997
    Co-Authors: Wassim M. Haddad, Joseph R. Corrado, Vijaysekhar Chellaboina, Dennis S. Bernstein
    Abstract:

    We explore the applicability of the implicit small gain guaranteed cost bound for Controller Synthesis. For flexibility in Controller Synthesis, we adopt the approach of fixed-structure Controller design which allows consideration of arbitrary Controller structures, including order, internal structure, and decentralization. A numerical example that has been addressed by means of alternative guaranteed cost bounds is presented to demonstrate the fixed-structure/implicit small gain approach to robust Controller Synthesis.