optimal control

Second-order analysis of optimal control problems with control and initial-final state constraints

  • Joseph Frédéric Bonnans
  • Nikolai Osmolovskii
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    This paper provides an analysis of Pontryagine mimina satisfying a quadratic growth condition, for optimal control problems of ordinary differential equations with constraints on initial-final state, as well as control constraints satisfying the uniform positive linear independence condition. Citation Rapport de Recherche INRIA 6707, Oct. 2008. Article Download View Second-order analysis of optimal control problems … Read more

    Necessary Conditions for the Impulsive Optimal Control of Multibody Mechanical Systems

  • Kerim Yunt
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , , , ,

    In this work, necessary conditions for the impulsive optimal control of multibody mechanical systems are stated. The conditions are obtained by the application subdifferential calculus techniques to extended-valued lower semi-continuous generalized Bolza functional that is evaluated on multiple intervals. Contrary to the approach in literature so far, the instant of possibly impulsive transition is considered … Read more

    Necessary optimality condition for Nonsmooth Switching Control problem

  • Shahlar Maharramov
    • Categories Nonsmooth Optimization Tags ,

    This paper is concerned with a class optimal switching nonsmoth optimal control problem is considered. Both the switching instants and the control function are to the chosen such that the cost functional is minimized.The necessary optimality conditions are derived by means of normal cone and Dubovitskii Milyutin theory. Citation Technical report 2007-3 Submited to the … Read more

    Stability and Sensitivity Analysis for Optimal Control Problems with a First-order State Constraint having (nonessential) Touch Points

  • Joseph Frédéric Bonnans
  • A. Hermant
    • Categories Infinite Dimensional Optimization Tags , , , ,

    The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessential) touch points, the arc structure of the trajectory is not stable. We show how to perform a sensitivity analysis that predicts which touch points will, under a small perturbation, become inactive, remain touch … Read more

    Primal-dual interior point methods for PDE-constrained optimization

  • Michael Ulbrich
  • Stefan Ulbrich
    • Categories Constrained Nonlinear Optimization, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in $L^p$. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier $L^\infty$-setting is analyzed, but also a more involved $L^q$-analysis, $q

    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

    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 Remarkable Property of the Dynamic Optimization Extremals

  • Delfim F. M. Torres
    • Categories Systems governed by Differential Equations Optimization Tags , , ,

    A dynamic optimization continuous problem poses the question of what is the optimal magnitude of a choice variable, at each point of time, in a given interval. To tackle such problems, three major approaches are available: dynamic programming; the calculus of variations; and the powerful optimal control approach. At the core of optimal control theory … Read more

    Sufficient Optimality in a Parabolic Control Problem

  • Hans D Mittelmann
  • Fredi Troeltzsch
    • Categories Applications - Science and Engineering, Optimization of Systems modeled by PDEs Tags , , ,

    We define a class of parabolic problems with control and state constraints and identify a problem within this class which possesses a locally unique critical point satisfying the second order sufficient optimality conditions. In this solution inequality constraints on the control are strongly active. The second derivative of the Lagrangian is not globally coercive. This … Read more

    Fast iterative solution of saddle point problems in optimal control based on wavelets

  • Angela Kunoth
    • Categories Systems governed by Differential Equations Optimization Tags , , , , , , , , , , ,

    In this paper, wavelet techniques are employed for the fast numerical solution of a control problem governed by an elliptic boundary value problem with boundary control. A quadratic cost functional involving natural norms of the state and the control is to be minimized. Firstly the constraint, the elliptic boundary value problem, is formulated in an … Read more