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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.
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https://hal.inria.fr/hal-00800395
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, March 13, 2013 - 4:13:58 PM
Last modification on : Tuesday, July 30, 2019 - 10:58:02 AM

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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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