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Nonlinearly constrained time-delayed optimal control problems. (English) Zbl 0812.49008

The Bolza optimal control problem for a retarded system with delay, presented both in control and state variable, is considered. The constraints on admissible trajectories are given by inequality phase constraints and by both equality and inequality terminal constraints. In order to develop a numerical algorithm, the controls are approximated by piecewise constant functions corresponding to the chosen time interval partition. For the in this way constructed finite dimensional extremal problem known mathematical programming algorithms are applied.
It is proved that under appropriate smoothness and stability assumptions the optimal value of the functional in the approximate problem converges to the optimal value in the initial problem as the diameter of partition tends to 0.
Two numerical examples are presented in order to illustrate the efficiency of the method.
Reviewer: D.Silin (Graz)

MSC:

49J25 Optimal control problems with equations with ret. arguments (exist.) (MSC2000)
49J15 Existence theories for optimal control problems involving ordinary differential equations

Software:

NLPQL
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References:

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