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The consistency problem in optimal control: the degenerate case
J. Cortés, S. Martínez
Reports on Mathematical Physics 51 (2/3) (2003), 171-186

Abstract

We examine the problem of the consistency of the second-order differential equations associated with optimal control problems. This problem can be treated in a presymplectic framework by means of a constraint algorithm. Two cases may arise: the regular one, already considered in the literature, and the degenerate one. The main contribution of this paper is the proposal of a discrete transition law for the optimal trajectories that reach a singular point. This discrete law respects both the geometry and the dynamical structure of the optimal control problem.

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