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An exact penalty method for free terminal time optimal control problem with continuous inequality constraints. (English) Zbl 1264.49036

The authors consider a class of optimal control problems with free terminal time and continuous inequality constraints. They approximate the control function with a piecewise-constant function and transform the inequality constraints into terminal equality constraints for an auxiliary differential system. The constraint optimization problem is transformed into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is solved by a gradient-based optimization technique. They show that this penalty function has continuous derivatives. For a sufficiently large and finite parameter, its local minimizer is feasible and also local minimizer of the constrained problem. Numerical simulations have been also performed.

MSC:

49M37 Numerical methods based on nonlinear programming
49J21 Existence theories for optimal control problems involving relations other than differential equations
90C30 Nonlinear programming

Software:

NLPQLP
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Full Text: DOI

References:

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