Second-order conditions for optimal control problems with mixed control-state constraints and control appearing linearly

Abstract : We study optimal control problems with a two-sided mixed control-state constraint and assume that the control variable appears linearly in both the system dynamics and constraints. By defining the control-state constraint as a new control variable, the optimal control problem is transformed into an optimal control problem with simple bounds on the new control variable. In view of Pontryagin's Minimum Principle, optimal controls of the transformed problem are concatenations of bang-bang or singular arcs. Second-order sufficient conditions (SSC) for such bang-singular controls have recently been given in the literature. We summarize results on SSC and illustrate their numerical verification on the optimal control of the Rayleigh equation for various bounds in a two-sided control-state constraint.
Type de document :
Communication dans un congrès
52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.514-519, 2013, Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC). 〈10.1109/CDC.2013.6759933〉
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https://hal.inria.fr/hal-01067546
Contributeur : Estelle Bouzat <>
Soumis le : mardi 23 septembre 2014 - 15:57:57
Dernière modification le : lundi 21 mars 2016 - 11:29:48

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Helmut Maurer, Nikolai Osmolovskii. Second-order conditions for optimal control problems with mixed control-state constraints and control appearing linearly. 52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.514-519, 2013, Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC). 〈10.1109/CDC.2013.6759933〉. 〈hal-01067546〉

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