Lipschitzian Regularity of Minimizers for Optimal Control Problems with Control-Affine Dynamics |
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Authors: | A. V. Sarychev D. F. M. Torres |
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Affiliation: | (1) Department of Mathematics, University of Aveiro, 3810 Aveiro, Portugal ansar@mat.ua.pt, delfim@mat.ua.pt, PT |
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Abstract: | We study the Lagrange Problem of Optimal Control with a functional and control-affine dynamics = f(t,x) + g(t,x)u and (a priori) unconstrained control u∈ bf R m . We obtain conditions under which the minimizing controls of the problem are bounded—a fact which is crucial for the applicability of many necessary optimality conditions, like, for example, the Pontryagin Maximum Principle. As a corollary we obtain conditions for the Lipschitzian regularity of minimizers of the Basic Problem of the Calculus of Variations and of the Problem of the Calculus of Variations with higher-order derivatives. Accepted 15 March 1999 |
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Keywords: | . Optimal control Calculus of variations Pontryagin Maximum Principle Boundedness of minimizers Nonlinear control-affine systems Lipschitzian regularity. AMS Classification. 49J15 49J30. |
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