Control Lyapunov Functions and Zubov's Method

For finite dimensional nonlinear control systems we study the relation between asymptotic null-controllability and control Lyapunov functions. It is shown that control Lyapunov functions may be constructed on the domain of asymptotic null-controllability as viscosity solutions of a first order PDE that generalizes Zubov's equation. The solution is also given as the value function of an optimal control problem from which several regularity results may be obtained. Key words. asymptotic nullcontrollability, control Lyapunov functions, Hamilton-Jacobi-Bellman equation, viscosity solutions, Zubov's method AMS subject classifications.

• Type: Journal
• Year: 2008
• Where: SIAMCO
• Authors: Fabio Camilli, Lars Grüne, Fabian Wirth
• Keywords: Asymptotic Null-controllability, Control Lyapunov Functions, Lyapunov Functions, SIAMCO 2008