Asymptotic controllability and optimal control

作者：Motta M; Rampazzo F^*

来源：Journal of Differential Equations, 2013, 254(7): 2744-2763.

DOI：10.1016/j.jde.2013.01.006

• Optimal control
• Asymptotic controllability
• Exit-time problems

We consider a control problem where the state must approach asymptotically a target C while paying an integral cost with a nonnegative Lagrangian l. The dynamics f is just continuous, and no assumptions are made on the zero level set of the Lagrangian I. Through an inequality involving a positive number (P) over bar (0) and a Minimum Restraint Function U = 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 U/(p) over bar (0). 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.

• 出版日期2013-4-1