A characteristics based curse-of-dimensionality-free approach for approximating control Lyapunov functions and feedback stabilization

Abstract

This paper develops a curse-of-dimensionality-free numerical approach to construct control Lyapunov functions (CLFs) and stabilizing feedback strategies for deterministic control systems described by ODEs. An extension of the Zubov method is used to represent a CLF as the value function for an appropriate infinite-horizon optimal control problem. The infinite-horizon stabilization problem is approximated by an exit time problem, with target set given by a sufficiently small closed neighborhood of the origin in the state space. In order to compute the related value function and optimal feedback control law separately at different initial states and thereby to attenuate the curse of dimensiona..