Abstract
A class of relaxed optimal control problems for ordinary differential equations with a state-space constraint is considered. The discretization by the control parametrization method, formerly proposed by Teo and Goh (Refs. 1, 2), is modified by admitting a tolerance in the state constraint, which enables one to prove a conditional convergence under certain additional qualification on the dynamics. Also, a counterexample is constructed, showing that the original, nonmodified discretization need not approximate the continuous problem.
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Communicated by A. Miele
The author is grateful to Professor K. L. Teo for useful comments on this paper.
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Roubćček, T. Convergent computational method for relaxed optimal control problems. J Optim Theory Appl 69, 589–603 (1991). https://doi.org/10.1007/BF00940690
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DOI: https://doi.org/10.1007/BF00940690