Asymptotic controllability and optimal control

Abstract

We consider a control problem where the state must reach asymptotically a target while paying an integral payoff with a non-negative Lagrangian. The dynamics is just continuous, and no assumptions are made on the zero level set of the Lagrangian. Through an inequality involving a positive number ${\bar{p}}_0$ and a Minimum Restraint Function $U=U(x)$ --a special type of Control Lyapunov Function-- we provide a condition implying that (i) the control system is asymptotically controllable, and (ii) the value function is bounded above by $U/{\bar{p}}_0$.

References in corpus (2)

• Global Asymptotic Controllability Implies Input to State Stabilization
• Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading

Cited by in corpus (5)

• Lyapunov-like functions involving Lie brackets
• The value function of an asymptotic exit-time optimal control problem
• HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation
• Asymptotic problems in optimal control with a vanishing Lagrangian and unbounded data
• GAC, savings, and unbounded inputs