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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.

  • 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.

  • further results on periodically time varying memory State Feedback Controller synthesis for discrete time linear systems
    Conference on Decision and Control, 2009
    Co-Authors: Yoshio Ebihara, Dimitri Peaucelle, Yuki Kuboyama, Tomomichi Hagiwara, Denis Arzelier
    Abstract:

    In this paper, we enhance the quality of our preceding results on periodically time-varying memory State-Feedback Controller (PTVMSFC) synthesis for discrete-time linear periodic/time-invariant systems. We firstly revisit PTVMSFC synthesis for certain systems and derive a necessary and sufficient LMI condition for the existence of the desired H ∞ -PTVMSFCs. Based on these LMIs, we next consider robust H ∞ -PTVMSFC synthesis for polytopic-type uncertain systems and demonstrate that we can obtain less conservative results. We finally derive a test to verify that the designed PTVMSFC is “exact” in the sense that it attains the best achievable robust H ∞ performance. This exactness verification test works fine in practice, and we show via numerical examples that exact robust control is indeed possible via PTVMSFCs, even for those problems where the standard static State-Feedback fails.

Denis Arzelier - One of the best experts on this subject based on the ideXlab platform.

  • 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.

  • further results on periodically time varying memory State Feedback Controller synthesis for discrete time linear systems
    Conference on Decision and Control, 2009
    Co-Authors: Yoshio Ebihara, Dimitri Peaucelle, Yuki Kuboyama, Tomomichi Hagiwara, Denis Arzelier
    Abstract:

    In this paper, we enhance the quality of our preceding results on periodically time-varying memory State-Feedback Controller (PTVMSFC) synthesis for discrete-time linear periodic/time-invariant systems. We firstly revisit PTVMSFC synthesis for certain systems and derive a necessary and sufficient LMI condition for the existence of the desired H ∞ -PTVMSFCs. Based on these LMIs, we next consider robust H ∞ -PTVMSFC synthesis for polytopic-type uncertain systems and demonstrate that we can obtain less conservative results. We finally derive a test to verify that the designed PTVMSFC is “exact” in the sense that it attains the best achievable robust H ∞ performance. This exactness verification test works fine in practice, and we show via numerical examples that exact robust control is indeed possible via PTVMSFCs, even for those problems where the standard static State-Feedback fails.

Xuejun Xie - One of the best experts on this subject based on the ideXlab platform.

Shakir Saat - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear State Feedback control for a class of polynomial nonlinear discrete time systems with norm bounded uncertainties an integrator approach
    Journal of The Franklin Institute-engineering and Applied Mathematics, 2013
    Co-Authors: Shakir Saat, Sing Kiong Nguang, Dan Huang, A H Hamidon
    Abstract:

    Abstract This paper investigates the problem of designing a nonlinear State Feedback Controller for a class of uncertain polynomial nonlinear discrete-time systems with norm-bounded uncertainties. In general, the problem of stabilising nonlinear discrete-time systems cannot be formulated as a convex problem. This is due to the fact that the Lyapunov function and the control input are not jointly convex, hence it cannot be solved by a semidefinite programming (SDP). In this paper, we propose a novel approach where an integrator is introduced to convexify this nonconvex Controller design problem. Furthermore, based on the sum of squares approach, sufficient conditions for the existence of a polynomial nonlinear State Feedback Controller for polynomial nonlinear discrete-time systems are given in terms of solvability of polynomial matrix inequalities. These inequalities are then solved by the sum of squares (SOS) solvers. Finally, numerical examples are provided to demonstrate the validity of this integrator approach.

  • nonlinear robust State Feedback control of uncertain polynomial discrete time systems an integral action approach
    International Conference on Control Automation Robotics and Vision, 2012
    Co-Authors: Shakir Saat, Sing Kiong Nguang, Guangbo Zeng
    Abstract:

    This paper examines the problem of designing a nonlinear robust State Feedback Controller for uncertain polynomial discrete-time systems. In general, this is a challenging Controller design problem due to the fact that the relation between Lyapunov function and the control input is not jointly convex, hence, this problem cannot be solved by a semidefinite programming (SDP). In this paper, a novel approach is proposed, where an integral action is incorporated into the Controller design so that a convex solution to the problem can be rendered. Based on the sum of squares (SOS) approach, sufficient conditions for the existence of a nonlinear State Feedback Controller for polynomial discrete-time systems are given in terms of solvability of polynomial matrix inequalities (PMIs), which can be solved by the recently developed SOS solver. Numerical examples are provided to demonstrate the validity of this integral action approach.

  • nonlinear State Feedback control for a class of polynomial discrete time systems with norm bounded uncertainties an integrator approach
    IFAC Proceedings Volumes, 2012
    Co-Authors: Shakir Saat, Sing Kiong Nguang, Dan Huang, Akshya Swain
    Abstract:

    Abstract This paper investigates the problem of designing a nonlinear State Feedback Controller for a class of uncertain polynomial discrete-time systems using rational Lyapunov functions. The uncertainty that under consideration is modelled as a norm-bounded uncertainty. In general, the problem of designing a Controller for polynomial discrete-time systems cannot be formulated as a convex problem. This is due to the fact that the Lyapunov function and the control input is not jointly convex, hence it cannot be solved by a semidefinite programming (SDP). In this paper, we propose a novel approach where an integrator is introduced to convexify the nonconvex Controller design problem, so that it can be solved easily by SDP. Furthermore, based on the sum of squares approach, sufficient conditions for the existence of a rational polynomial State Feedback Controller for a polynomial discrete-time systems are given in terms of solvability of polynomial matrix inequalities. These inequalities are then solved by the recently developed sum of squares (SOS) solvers. Finally, numerical example is provided to demonstrate the validity of this integrator approach.

Gerd Hirzinger - One of the best experts on this subject based on the ideXlab platform.

  • MIMO State Feedback Controller for a Flexible Joint Robot with Strong Joint Coupling
    Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
    Co-Authors: Luc Le Tien, Alin Albu Schaffer, Gerd Hirzinger
    Abstract:

    The paper describes the modeling and control of a robot with flexible joints (the DLR medical robot), which has strong mechanical couplings between pairs of joints realized with a differential gear-box. Because of this coupling, Controllers developed before for the DLR light-weight robots cannot be directly applied. The previous control approach is extended in order to allow a multi-input-multi-output (MIMO) design for the strongly coupled joints. Asymptotic stability is shown for the MIMO Controller. Finally, experimental results with the DLR medical robot are presented.

  • a globally stable State Feedback Controller for flexible joint robots
    Advanced Robotics, 2001
    Co-Authors: Alin Albuschaffer, Gerd Hirzinger
    Abstract:

    The paper addresses the problem of controlling the joints of a flexible joint robot with a State Feedback Controller and proposes a gradual way of extending such a Controller towards the complete decoupling of the robot dynamics. The global asymptotic stability for the State Feedback Controller with gravity compensation is proven, followed by some theoretical remarks on its passivity properties. By proper parameterization, the proposed Controller structure can implement a position, a stiffness or a torque Controller. Experimental results on the DLR lightweight robots validate the method.

  • State Feedback Controller for flexible joint robots: a globally stable approach implemented on DLR's light-weight robots
    Proceedings. 2000 IEEE RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113), 2000
    Co-Authors: A. Albu-schaffer, Gerd Hirzinger
    Abstract:

    Addresses the problem of controlling the joints of a flexible joint robot with a State Feedback Controller and proposes a gradual way of extending such a Controller towards Feedback linearization. The global asymptotic stability for the State Feedback Controller with gravity compensation is proven. Experimental results on the DLR light-weight robots validate the method.