Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal control Part II: Numerical approach

Abstract

This paper continues the study (Yegorov, Dower, and Grüne et al.) and develops a curse-of-dimensionality-free numerical approach to feedback stabilization, whose theoretical foundation was built in Yegorov et al. and involved the characterization of control Lyapunov functions (CLFs) via exit-time optimal control. First, we describe an auxiliary linearization-based technique for the construction of a local CLF and discuss how to determine its appropriate sublevel set that can serve as the terminal set in the exit-time optimal control problem leading to a global or semi-global CLF. Next, the curse of complexity is addressed with regard to the approximation of CLFs and associated feedback strat..