Control Lyapunov Functions and Zubov's Method

Titelangaben

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Control Lyapunov Functions and Zubov's Method.
In: SIAM Journal on Control and Optimization. Bd. 47 (2008) Heft 1 . - S. 301-326.
ISSN 1095-7138
DOI: https://doi.org/10.1137/06065129X

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Abstract

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.