Control Applications

On Time-Invariant Purified-Output-Based Discrete Time Control

  • Aharon Ben-Tal
  • Stephen Boyd
  • Arkadi Nemirovski
    • Categories Control Applications, Convex Optimization, Semi-definite Programming Tags , ,

    In http://www.optimizationonline.org/DB_HTML/2005/05/1136.html 05/25/05, we have demonstrated that the family of all affine non-anticipative output-based control laws in a discrete time linear dynamical system affected by uncertain disturbances is equivalent, as far as state-control trajectories are concerned, to the family of all affine non-anticipative “purified-output-based” control laws. The advantage of the latter representation of affine controls … Read more

    Efficient Robust Optimization for Robust Control with Constraints

  • Paul J. Goulart
  • Daniel Ralph
  • EC Kerrigan
    • Categories Control Applications, Robust Optimization Tags , , , , ,

    This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques … Read more

    Nonlinear optimal control: Numerical approximations via moments and LMI-relaxations

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Christophe Prieur
    • Categories Control Applications, Systems governed by Differential Equations Optimization

    We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments. CitationLAAS report … Read more

    Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems

  • Aharon Ben-Tal
  • Stephen Boyd
  • Arkadi Nemirovski
    • Categories Control Applications, Robust Optimization Tags , ,

    In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance … Read more

    Analysis of a Belgian Chocolate Stabilization Problem

  • James V. Burke
  • Didier Henrion
  • Adrian Lewis
  • Michael L. Overton
    • Categories Control Applications, Nonsmooth Optimization Tags , , ,

    We give a detailed numerical and theoretical analysis of a stabilization problem posed by V. Blondel in 1994. Our approach illustrates the effectiveness of a new gradient sampling algorithm for finding local optimizers of nonsmooth, nonconvex optimization problems arising in control, as well as the power of nonsmooth analysis for understanding variational problems involving polynomial … Read more

    Convergent relaxations of polynomial matrix inequalities and static output feedback

  • Didier Henrion
  • Jean-Bernard Lasserre
    • Categories Control Applications, Semi-definite Programming Tags , , ,

    Using a moment interpretation of recent results on sum-of-squares decompositions of non-negative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve non-convex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to … Read more

    Optimal Nodal Control of Networked Hyperbolic Systems: Evaluation of Derivatives

  • Martin Gugat
    • Categories Applications - Science and Engineering, Control Applications, Optimization of Systems modeled by PDEs Tags , , , , ,

    We consider a networked system defined on a graph where each edge corresponds to a quasilinear hyperbolic system with space dimension one. At the nodes, the system is governed by algebraic node conditions. The system is controlled at the nodes of the graph. Optimal control problems for systems of this type arise in the operation … Read more

    A survey of the S-lemma

  • Imre Pólik
  • Tamás Terlaky
    • Categories Control Applications, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , , ,

    In this survey we review the many faces of the S-lemma, a result about the correctness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry and linear algebra as well. These were active research areas, but as … Read more

    Fuzzy Modeling with Adaptive Simulated Annealing

  • Hime Aguiar e Oliveira Jr.
    • Categories Control Applications, Global Optimization Applications

    A new method for data-based fuzzy system modeling is presented. The approach uses Takagi-Sugeno models and Adaptive Simulated Annealing (ASA) to achieve its goal . The problem to solve is well defined – given a training set containing a finite number of input-output pairs, construct a fuzzy system that approximates the behavior of the real … Read more

    Implementation of Infinite Dimensional Interior Point Method for Solving Multi-criteria Linear-Quadratic Control Problem

  • Leonid Faybusovich
  • Takashi Tsuchiya
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We describe an implementation of an infinite-dimensional primal-dual algorithm based on the Nesterov-Todd direction. Several applications to both continuous and discrete-time multi-criteria linear-quadratic control problems and linear-quadratic control problem with quadratic constraints are described. Numerical results show a very fast convergence (typically, within 3-4 iterations) to optimal solutions CitationPreprint, May, 2004, University of Notre DameArticleDownload … Read more