Control Lyapunov Functions and Zubov's Method

L. Grüne, F. Camilli, F. Wirth: Control Lyapunov Functions and Zubov's Method
SIAM Journal on Control and Optimization 47, 301 - 326, 2008

DOI: 10.1137/06065129X
Keywords: asymptotic null-controllability; control Lyapunov functions; Hamilton-Jacobi-Bellman equation; viscosity solutions; Zubov's method
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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.

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