Asymptotic controllability and optimal control

Abstract : We consider a control problem where the state must approach asymptotically a target C while paying an integral cost with a non-negative Lagrangian l. The dynamics f is just continuous, and no assumptions are made on the zero level set of the Lagrangian l. Through an inequality involving a positive number and a Minimum Restraint FunctionU=U(x) - a special type of Control Lyapunov Function - we provide a condition implying that (i) the system is asymptotically controllable, and (ii) the value function is bounded by . The result has significant consequences for the uniqueness issue of the corresponding Hamilton-Jacobi equation. Furthermore it may be regarded as a first step in the direction of a feedback construction.
Type de document :
Article dans une revue
Journal of Differential Equations, Elsevier, 2013, 254 (7), pp.2744-2763. 〈10.1016/j.jde.2013.01.006〉
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Soumis le : mercredi 13 mars 2013 - 16:13:58
Dernière modification le : jeudi 14 juin 2018 - 10:54:02

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Monica Motta, Franco Rampazzo. Asymptotic controllability and optimal control. Journal of Differential Equations, Elsevier, 2013, 254 (7), pp.2744-2763. 〈10.1016/j.jde.2013.01.006〉. 〈hal-00800395〉



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