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Title: Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics
Author: Sarychev, A.V.
Torres, D.F.M.
Keywords: Optimal control
Calculus of variations
Pontryagin Maximum Principle
Boundedness of minimizers
Nonlinear control-affine systems
Lipschitzian regularity
Issue Date: 2000
Publisher: Springer Verlag
Abstract: We study the Lagrange Problem of Optimal Control with a functional ∫abL(t, x(t), u(t))dt and control-affine dynamics x = f(t, x)+g(t, x)u and (a priori) unconstrained control u∈Rm. 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.
Peer review: yes
ISSN: 0095-4616
Appears in Collections:MAT - Artigos

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