Asymptotic controllability and optimal control - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Differential Equations Year : 2013

Asymptotic controllability and optimal control


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.

Dates and versions

hal-00800395 , version 1 (13-03-2013)



Monica Motta, Franco Rampazzo. Asymptotic controllability and optimal control. Journal of Differential Equations, 2013, 254 (7), pp.2744-2763. ⟨10.1016/j.jde.2013.01.006⟩. ⟨hal-00800395⟩
94 View
0 Download



Gmail Facebook Twitter LinkedIn More