The Experts below are selected from a list of 129 Experts worldwide ranked by ideXlab platform

Ian A Hiskens - One of the best experts on this subject based on the ideXlab platform.

  • parametric dependence of large disturbance response and relationship to stability boundary
    Conference on Decision and Control, 2017
    Co-Authors: Michael W Fisher, Ian A Hiskens
    Abstract:

    This paper considers a system of ordinary differential equations subject to a Parameter-dependent disturbance. The goal is to find the boundary in Parameter space between Parameter values for which the system will recover from the disturbance to a Desired stable equilibrium point, and Parameter values for which it will not recover. If the system state when the disturbance clears, call it the initial condition, depends continuously on Parameter value, then it seems plausible that this Parameter space boundary would consist of Parameter values whose corresponding initial conditions lie on the boundary of the region of attraction (RoA) of the Desired stable equilibrium point (SEP). Unfortunately, this is not true in general since, even when the system's vector field varies smoothly with Parameter value, the boundary of the RoA of the SEP may not vary even continuously with respect to small Parameter variations. This work shows that, for a large class of vector fields which generalize Morse-Smale vector fields, the RoA boundary varies continuously in an appropriate sense with respect to small Parameter variations. Furthermore, it has been shown elsewhere that the RoA boundary for these vector fields is equal to the union of the stable manifolds of the equilibria and periodic orbits they contain. A complete argument is provided here that this decomposition into stable manifolds persists under small changes in Parameter for the vector fields under consideration. The above results are applied to provide a theoretical basis for a numerical algorithm which computes Parameter values which lie on the Desired Parameter space boundary.

  • CDC - Parametric dependence of large disturbance response and relationship to stability boundary
    2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017
    Co-Authors: Michael W Fisher, Ian A Hiskens
    Abstract:

    This paper considers a system of ordinary differential equations subject to a Parameter-dependent disturbance. The goal is to find the boundary in Parameter space between Parameter values for which the system will recover from the disturbance to a Desired stable equilibrium point, and Parameter values for which it will not recover. If the system state when the disturbance clears, call it the initial condition, depends continuously on Parameter value, then it seems plausible that this Parameter space boundary would consist of Parameter values whose corresponding initial conditions lie on the boundary of the region of attraction (RoA) of the Desired stable equilibrium point (SEP). Unfortunately, this is not true in general since, even when the system's vector field varies smoothly with Parameter value, the boundary of the RoA of the SEP may not vary even continuously with respect to small Parameter variations. This work shows that, for a large class of vector fields which generalize Morse-Smale vector fields, the RoA boundary varies continuously in an appropriate sense with respect to small Parameter variations. Furthermore, it has been shown elsewhere that the RoA boundary for these vector fields is equal to the union of the stable manifolds of the equilibria and periodic orbits they contain. A complete argument is provided here that this decomposition into stable manifolds persists under small changes in Parameter for the vector fields under consideration. The above results are applied to provide a theoretical basis for a numerical algorithm which computes Parameter values which lie on the Desired Parameter space boundary.

Michael W Fisher - One of the best experts on this subject based on the ideXlab platform.

  • parametric dependence of large disturbance response and relationship to stability boundary
    Conference on Decision and Control, 2017
    Co-Authors: Michael W Fisher, Ian A Hiskens
    Abstract:

    This paper considers a system of ordinary differential equations subject to a Parameter-dependent disturbance. The goal is to find the boundary in Parameter space between Parameter values for which the system will recover from the disturbance to a Desired stable equilibrium point, and Parameter values for which it will not recover. If the system state when the disturbance clears, call it the initial condition, depends continuously on Parameter value, then it seems plausible that this Parameter space boundary would consist of Parameter values whose corresponding initial conditions lie on the boundary of the region of attraction (RoA) of the Desired stable equilibrium point (SEP). Unfortunately, this is not true in general since, even when the system's vector field varies smoothly with Parameter value, the boundary of the RoA of the SEP may not vary even continuously with respect to small Parameter variations. This work shows that, for a large class of vector fields which generalize Morse-Smale vector fields, the RoA boundary varies continuously in an appropriate sense with respect to small Parameter variations. Furthermore, it has been shown elsewhere that the RoA boundary for these vector fields is equal to the union of the stable manifolds of the equilibria and periodic orbits they contain. A complete argument is provided here that this decomposition into stable manifolds persists under small changes in Parameter for the vector fields under consideration. The above results are applied to provide a theoretical basis for a numerical algorithm which computes Parameter values which lie on the Desired Parameter space boundary.

  • CDC - Parametric dependence of large disturbance response and relationship to stability boundary
    2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017
    Co-Authors: Michael W Fisher, Ian A Hiskens
    Abstract:

    This paper considers a system of ordinary differential equations subject to a Parameter-dependent disturbance. The goal is to find the boundary in Parameter space between Parameter values for which the system will recover from the disturbance to a Desired stable equilibrium point, and Parameter values for which it will not recover. If the system state when the disturbance clears, call it the initial condition, depends continuously on Parameter value, then it seems plausible that this Parameter space boundary would consist of Parameter values whose corresponding initial conditions lie on the boundary of the region of attraction (RoA) of the Desired stable equilibrium point (SEP). Unfortunately, this is not true in general since, even when the system's vector field varies smoothly with Parameter value, the boundary of the RoA of the SEP may not vary even continuously with respect to small Parameter variations. This work shows that, for a large class of vector fields which generalize Morse-Smale vector fields, the RoA boundary varies continuously in an appropriate sense with respect to small Parameter variations. Furthermore, it has been shown elsewhere that the RoA boundary for these vector fields is equal to the union of the stable manifolds of the equilibria and periodic orbits they contain. A complete argument is provided here that this decomposition into stable manifolds persists under small changes in Parameter for the vector fields under consideration. The above results are applied to provide a theoretical basis for a numerical algorithm which computes Parameter values which lie on the Desired Parameter space boundary.

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

F. Jabbari - One of the best experts on this subject based on the ideXlab platform.

  • Scheduled controllers for disturbance attenuation of systems with bounded inputs
    Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
    Co-Authors: Sharad Srivastava, F. Jabbari
    Abstract:

    A class of scheduled state feedback controllers are developed for disturbance attenuation in systems with bounded actuators. The scheduling Parameter, obtained from a set of Parameterized ellipsoids, is a measure of the system response and allows the controller to adjust to lower controller gains as the states become larger. The controller is obtained by approximating the Desired Parameter dependent variables with linear spline functions.

Roni Khazaka - One of the best experts on this subject based on the ideXlab platform.

  • Parameterized model order reduction techniques for fem based full wave analysis
    IEEE Transactions on Advanced Packaging, 2009
    Co-Authors: Madhusudanan Sampath, Anestis Dounavis, Roni Khazaka
    Abstract:

    As operating frequencies increase full wave methods such as the finite element method (FEM) become necessary for the analysis of high-frequency circuit structures. Such techniques result in very large systems of equations, and model order reduction (MOR) was proven to be very effective in combating such increased complexity. Using traditional MOR, one has to generate a new reduced model each time a design Parameter is modified, thus significantly reducing the CPU efficiency. In this paper, a multidimensional Krylov subspace method is proposed to perform reduction directly on the vector wave equation based FEM system and to generate parametric reduced order models that are valid over the Desired Parameter range without the need to redo the reduction. In order to accomplish this, second-order Arnoldi methods are extended to include design Parameters such as material properties, and geometrical Parameters in the reduced order model. In addition, multidimensional moment matching technique is used to address the Krylov incompatibility of FEM problems which include arbitrary frequency dependence in the system. This technique results in significant CPU savings and enables applications such as optimization and design space exploration.

  • Generation of Geometrically Parameterized Reduced Order Models for Full Wave Problems
    2006 IEEE Electrical Performane of Electronic Packaging, 2006
    Co-Authors: M.k. Sampath, Anestis Dounavis, Roni Khazaka
    Abstract:

    In this paper, an approach for generating geometrically Parameterized reduced order models for full wave finite element method problems is presented. The proposed Parameterized model order reduction technique is based on multidimensional congruent transformation techniques and generates geometrically Parameterized reduced order models that are valid over the Desired Parameter range without the need to redo the reduction. The proposed approach enables applications such optimization and design space exploration and results in significant CPU savings.