On Global Optimality Conditions for Nonlinear Optimal Control Problems |
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Authors: | FH Clarke J-B Hiriart-Urruty YuS Ledyaev |
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Institution: | (1) Institut Desargues, Université Lyon I (Bâtiment 101), 69622 Villeurbanne, France (e-mail: Email;(2) Université Paul Sabatier, 31062 Toulouse, France (e-mail: Email;(3) Steklov Institute of Mathematics, Moscow, 117966, Russia (e-mail: Email |
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Abstract: | Let a trajectory and control pair
maximize globally the functional g(x(T)) in the basic optimal control problem. Then (evidently) any pair (x,u) from the level set of the functional g corresponding to the value g(
(T)) is also globally optimal and satisfies the Pontryagin maximum principle. It is shown that this necessary condition for global optimality of
turns out to be a sufficient one under the additional assumption of nondegeneracy of the maximum principle for every pair (x,u) from the above-mentioned level set. In particular, if the pair
satisfies the Pontryagin maximum principle which is nondegenerate in the sense that for the Hamiltonian H, we have along the pair
on 0,T], and if there is no another pair (x,u) such that g(x(T))=g(
(T)), then
is a global maximizer. |
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Keywords: | Optimal control Pontryagin maximum principle Global optimality |
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