Discrete approximation of relaxed optimal control problems

  • I. Chryssoverghi
  • A. Bacopoulos
Contributed Papers


We consider a general nonlinear optimal control problem for systems governed by ordinary differential equations with terminal state constraints. No convexity assumptions are made. The problem, in its so-called relaxed form, is discretized and necessary conditions for discrete relaxed optimality are derived. We then prove that discrete optimality [resp., extremality] in the limit carries over to continuous optimality [resp., extremality]. Finally, we prove that limits of sequences of Gamkrelidze discrete relaxed controls can be approximated by classical controls.

Key Words

Optimal control nonlinear systems discretization nonconvexity relaxed controls approximation 


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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • I. Chryssoverghi
    • 1
  • A. Bacopoulos
    • 1
  1. 1.Department of MathematicsNational Technical UniversityAthensGreece

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