A sufficient condition for local semiconcavity of value function of nonlinear optimal regulator

This paper presents a sufficient condition that the value functions of nonlinear optimal regulator problem are locally semiconcave. Semiconcave function is a continuous, and Lipschitz function. Semiconcave Lyapunov function is useful to analyze and design control systems with discontinuous feedback control. In this paper, a sufficient condition for the semiconcavity of value function is shown, that is, a sufficient condition for the existence of a semiconcave control Lyapunov function.