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Kazuyuki Aihara - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic Robust Bifurcation Analysis
    Analysis and Control of Complex Dynamical Systems, 2015
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    We propose a new concept of dynamic robust Bifurcation Analysis for uncertain dynamical systems. An uncertain system is described by a feedback form composed of a nonlinear dynamical system and a dynamic uncertainty that is defined by a set of differential equations. For such an uncertain system, a Bifurcation point can be uncertain as well. Therefore, we formulate a dynamic robust Bifurcation Analysis problem of identifying the set of all potential Bifurcation points. To this end, first, we study equilibrium Analysis to evaluate the existence and location of equilibria. Next, we derive a condition for robust hyperbolicity of the evaluated set of potential equilibrium points. On the basis of the condition, we propose a method for identifying the set of potential Bifurcation points. Finally, illustrative examples for robustness Analysis of normal forms for various Bifurcations are presented.

  • Robust Bifurcation Analysis of systems with dynamic uncertainties
    International Journal of Bifurcation and Chaos, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    In this paper, we propose in uncertain dynamical systems a novel method for identifying the region that includes all possible Bifurcation boundaries. First, we formulate a robust Bifurcation Analysis problem for parameter-dependent differential equations with dynamic uncertainties. Next, to solve this problem, we give stability and instability conditions for the uncertain system. Finally, on the basis of these conditions, we propose a method for solving the robust Bifurcation Analysis problem.

  • an instability condition for uncertain systems toward robust Bifurcation Analysis
    European Control Conference, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Takayuki Arai, Kazuyuki Aihara
    Abstract:

    In this paper, we consider instability Analysis of uncertain feedback systems. First, we present an instability counterpart of the small gain stability theorem. Based on the instability theorem, we solve the problem of instability Analysis for systems with dynamic uncertainties. Then, we propose a novel concept of robust Bifurcation Analysis. An illustrative example is presented for Bifurcation Analysis of uncertain genetic network models.

  • ECC - An instability condition for uncertain systems toward robust Bifurcation Analysis
    2013 European Control Conference (ECC), 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Takayuki Arai, Kazuyuki Aihara
    Abstract:

    In this paper, we consider instability Analysis of uncertain feedback systems. First, we present an instability counterpart of the small gain stability theorem. Based on the instability theorem, we solve the problem of instability Analysis for systems with dynamic uncertainties. Then, we propose a novel concept of robust Bifurcation Analysis. An illustrative example is presented for Bifurcation Analysis of uncertain genetic network models.

  • CDC - Robust Bifurcation Analysis based on the Nyquist stability criterion
    52nd IEEE Conference on Decision and Control, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    In this paper, we propose a novel method for robust Bifurcation Analysis of systems with dynamic uncertainties. First, we formulate a robust Bifurcation Analysis problem for parameter-dependent systems with norm-bounded uncertainties. Next, to solve this problem, we define a new concept of robust hyperbolicity of an equilibrium that for any uncertainty an uncertain linear system has no neutral pole and the number of unstable poles is constant. A necessary and sufficient condition for the robust hyperbolicity is derived from the Nyquist stability criterion. On the basis of the condition, we propose a method for identifying the region that consists of all potential Bifurcation boundaries. Finally, robustness of a gene-metabolic oscillator with dynamic uncertainties is investigated by using the proposed method.

J H Sluyters - One of the best experts on this subject based on the ideXlab platform.

Masaki Inoue - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic Robust Bifurcation Analysis
    Analysis and Control of Complex Dynamical Systems, 2015
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    We propose a new concept of dynamic robust Bifurcation Analysis for uncertain dynamical systems. An uncertain system is described by a feedback form composed of a nonlinear dynamical system and a dynamic uncertainty that is defined by a set of differential equations. For such an uncertain system, a Bifurcation point can be uncertain as well. Therefore, we formulate a dynamic robust Bifurcation Analysis problem of identifying the set of all potential Bifurcation points. To this end, first, we study equilibrium Analysis to evaluate the existence and location of equilibria. Next, we derive a condition for robust hyperbolicity of the evaluated set of potential equilibrium points. On the basis of the condition, we propose a method for identifying the set of potential Bifurcation points. Finally, illustrative examples for robustness Analysis of normal forms for various Bifurcations are presented.

  • Robust Bifurcation Analysis of systems with dynamic uncertainties
    International Journal of Bifurcation and Chaos, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    In this paper, we propose in uncertain dynamical systems a novel method for identifying the region that includes all possible Bifurcation boundaries. First, we formulate a robust Bifurcation Analysis problem for parameter-dependent differential equations with dynamic uncertainties. Next, to solve this problem, we give stability and instability conditions for the uncertain system. Finally, on the basis of these conditions, we propose a method for solving the robust Bifurcation Analysis problem.

  • an instability condition for uncertain systems toward robust Bifurcation Analysis
    European Control Conference, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Takayuki Arai, Kazuyuki Aihara
    Abstract:

    In this paper, we consider instability Analysis of uncertain feedback systems. First, we present an instability counterpart of the small gain stability theorem. Based on the instability theorem, we solve the problem of instability Analysis for systems with dynamic uncertainties. Then, we propose a novel concept of robust Bifurcation Analysis. An illustrative example is presented for Bifurcation Analysis of uncertain genetic network models.

  • ECC - An instability condition for uncertain systems toward robust Bifurcation Analysis
    2013 European Control Conference (ECC), 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Takayuki Arai, Kazuyuki Aihara
    Abstract:

    In this paper, we consider instability Analysis of uncertain feedback systems. First, we present an instability counterpart of the small gain stability theorem. Based on the instability theorem, we solve the problem of instability Analysis for systems with dynamic uncertainties. Then, we propose a novel concept of robust Bifurcation Analysis. An illustrative example is presented for Bifurcation Analysis of uncertain genetic network models.

  • CDC - Robust Bifurcation Analysis based on the Nyquist stability criterion
    52nd IEEE Conference on Decision and Control, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    In this paper, we propose a novel method for robust Bifurcation Analysis of systems with dynamic uncertainties. First, we formulate a robust Bifurcation Analysis problem for parameter-dependent systems with norm-bounded uncertainties. Next, to solve this problem, we define a new concept of robust hyperbolicity of an equilibrium that for any uncertainty an uncertain linear system has no neutral pole and the number of unstable poles is constant. A necessary and sufficient condition for the robust hyperbolicity is derived from the Nyquist stability criterion. On the basis of the condition, we propose a method for identifying the region that consists of all potential Bifurcation boundaries. Finally, robustness of a gene-metabolic oscillator with dynamic uncertainties is investigated by using the proposed method.

Marc T M Koper - One of the best experts on this subject based on the ideXlab platform.

Jun-ichi Imura - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic Robust Bifurcation Analysis
    Analysis and Control of Complex Dynamical Systems, 2015
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    We propose a new concept of dynamic robust Bifurcation Analysis for uncertain dynamical systems. An uncertain system is described by a feedback form composed of a nonlinear dynamical system and a dynamic uncertainty that is defined by a set of differential equations. For such an uncertain system, a Bifurcation point can be uncertain as well. Therefore, we formulate a dynamic robust Bifurcation Analysis problem of identifying the set of all potential Bifurcation points. To this end, first, we study equilibrium Analysis to evaluate the existence and location of equilibria. Next, we derive a condition for robust hyperbolicity of the evaluated set of potential equilibrium points. On the basis of the condition, we propose a method for identifying the set of potential Bifurcation points. Finally, illustrative examples for robustness Analysis of normal forms for various Bifurcations are presented.

  • Robust Bifurcation Analysis of systems with dynamic uncertainties
    International Journal of Bifurcation and Chaos, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    In this paper, we propose in uncertain dynamical systems a novel method for identifying the region that includes all possible Bifurcation boundaries. First, we formulate a robust Bifurcation Analysis problem for parameter-dependent differential equations with dynamic uncertainties. Next, to solve this problem, we give stability and instability conditions for the uncertain system. Finally, on the basis of these conditions, we propose a method for solving the robust Bifurcation Analysis problem.

  • an instability condition for uncertain systems toward robust Bifurcation Analysis
    European Control Conference, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Takayuki Arai, Kazuyuki Aihara
    Abstract:

    In this paper, we consider instability Analysis of uncertain feedback systems. First, we present an instability counterpart of the small gain stability theorem. Based on the instability theorem, we solve the problem of instability Analysis for systems with dynamic uncertainties. Then, we propose a novel concept of robust Bifurcation Analysis. An illustrative example is presented for Bifurcation Analysis of uncertain genetic network models.

  • ECC - An instability condition for uncertain systems toward robust Bifurcation Analysis
    2013 European Control Conference (ECC), 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Takayuki Arai, Kazuyuki Aihara
    Abstract:

    In this paper, we consider instability Analysis of uncertain feedback systems. First, we present an instability counterpart of the small gain stability theorem. Based on the instability theorem, we solve the problem of instability Analysis for systems with dynamic uncertainties. Then, we propose a novel concept of robust Bifurcation Analysis. An illustrative example is presented for Bifurcation Analysis of uncertain genetic network models.

  • CDC - Robust Bifurcation Analysis based on the Nyquist stability criterion
    52nd IEEE Conference on Decision and Control, 2013
    Co-Authors: Masaki Inoue, Jun-ichi Imura, Kenji Kashima, Kazuyuki Aihara
    Abstract:

    In this paper, we propose a novel method for robust Bifurcation Analysis of systems with dynamic uncertainties. First, we formulate a robust Bifurcation Analysis problem for parameter-dependent systems with norm-bounded uncertainties. Next, to solve this problem, we define a new concept of robust hyperbolicity of an equilibrium that for any uncertainty an uncertain linear system has no neutral pole and the number of unstable poles is constant. A necessary and sufficient condition for the robust hyperbolicity is derived from the Nyquist stability criterion. On the basis of the condition, we propose a method for identifying the region that consists of all potential Bifurcation boundaries. Finally, robustness of a gene-metabolic oscillator with dynamic uncertainties is investigated by using the proposed method.