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Discrete approximation of relaxed optimal control problems

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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.

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Communicated by D. Q. Mayne

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Chryssoverghi, I., Bacopoulos, A. Discrete approximation of relaxed optimal control problems. J Optim Theory Appl 65, 395–407 (1990).

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Key Words

  • Optimal control
  • nonlinear systems
  • discretization
  • nonconvexity
  • relaxed controls
  • approximation