Classical and Relaxed Progressively Refining Discretization-Optimization Methods for Optimal Control Problems Defined by Ordinary Differential Equations

  • I. Chryssoverghi
  • J. Coletsos
  • B. Kokkinis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

Abstract

An optimal control problem is considered, for systems defined by nonlinear ordinary differential equations, with control and pointwise state constraints. Since the problem may have no classical solutions, it is also formulated in the relaxed form. Various necessary/sufficient conditions for optimality are first given for both formulations. In order to solve these problems numerically, we then propose a discrete penalized gradient projection method generating classical controls, and a discrete penalised conditional descent method generating relaxed controls. In both methods, the discretization procedure is progressively refining in order to achieve efficiency with reduced computational cost. Results are given concerning the behaviour in the limit of these methods. Finally, numerical examples are provided.

Keywords

Optimal Control Problem State Constraint Nonlinear Ordinary Differential Equation Initial Control Classical Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • I. Chryssoverghi
    • 1
  • J. Coletsos
    • 1
  • B. Kokkinis
    • 1
  1. 1.Department of Mathematics, School of Applied Mathematics and PhysicsNational Technical University of AthensAthensGreece

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