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When does relaxation reduce the minimum cost of an optimal control problem?

Abstract : Relaxation is a regularization procedure used in optimal control, involving the replacement of velocity sets by their convex hulls, to ensure the existence of a minimizer. It can be an important step in the construction of sub-optimal controls for the original, unrelaxed, optimal control problem (which may not have a minimizer), based on obtaining a minimizer for the relaxed problem and approximating it. In some cases the infimum cost of the unrelaxed problem is strictly greater than the infimum cost over relaxed state trajectories; there is a need to identify such situations because then the above procedure fails. Following on from earlier work by Warga, we explore the relation between, on the one hand, non-coincidence of the minimum cost of the optimal control and its relaxation and, on the other, abnormality of necessary conditions (in the sense that they take a degenerate form in which the cost multiplier set to zero).
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https://hal.inria.fr/hal-01067548
Contributor : Estelle Bouzat <>
Submitted on : Tuesday, September 23, 2014 - 4:00:47 PM
Last modification on : Monday, March 21, 2016 - 5:50:25 PM

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Michele Palladino, Richard Vinter. When does relaxation reduce the minimum cost of an optimal control problem?. 52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.526-531, ⟨10.1109/CDC.2013.6759935⟩. ⟨hal-01067548⟩

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