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An exact penalty method for constrained optimal control problems

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Abstract

We develop a theoretical framework for constrained optimal control problems. Using an exact penalty method, the differential equation as well as the constraints are handled to obtain an abstract nonsmooth infinite dimensional optimization problem. By tools of nonsmooth analysis theory in infinite dimensional spaces, we investigate the relation between the stationary points of the obtained nondifferentiable optimization problem and those of the constrained optimal control problem. An algorithm to minimize the unconstrained problem combined the penalty function and the projection method is also given.

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Acknowledgements

The authors are grateful to anonymous reviewers for valuable remarks and comments, which significantly contributed to the quality of the paper.

Funding

This work was supported by Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO) and the Algerian research Project: PRFU, No. C00L03ES310120180002.

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Authors and Affiliations

  1. Department of Systems Engineering (Ex. Department of Mathematics and informatics), National Polytechnic School of Oran - Maurice Audin, BP 1523, Oran-El M’naouar, 31000, Oran, Algeria

    Abdelwahhab Hammoudi & Mohammed Benharrat

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  1. Abdelwahhab Hammoudi
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  2. Mohammed Benharrat
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Correspondence to Mohammed Benharrat.

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Hammoudi, A., Benharrat, M. An exact penalty method for constrained optimal control problems. Rend. Circ. Mat. Palermo, II. Ser 70, 275–293 (2021). https://doi.org/10.1007/s12215-020-00496-4

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