Mathematical Control and Related Fields (MCRF)

Zubov's equation for state-constrained perturbed nonlinear systems

Pages: 55 - 71, Volume 5, Issue 1, March 2015      doi:10.3934/mcrf.2015.5.55

       Abstract        References        Full Text (1825.6K)       Related Articles       

Lars Grüne - Mathematisches Institute, Universität Bayreuth, 95440 Bayreuth, Germany (email)
Hasnaa Zidani - Mathematics Department - UMA, ENSTA ParisTech, 91762 Palaiseau, France (email)

Abstract: The paper gives a characterization of the uniform robust domain of attraction for a finite non-linear controlled system subject to perturbations and state constraints. We extend the Zubov approach to characterize this domain by means of the value function of a suitable infinite horizon state-constrained control problem which at the same time is a Lyapunov function for the system. We provide associated Hamilton-Jacobi-Bellman equations and prove existence and uniqueness of the solutions of these generalized Zubov equations.

Keywords:  Domain of attraction, state-constrained nonlinear systems, Zubov's approach, Hamilton-Jacobi equations, viscosity solution.
Mathematics Subject Classification:  93D09, 35F21, 49L25.

Received: October 2013;      Revised: February 2014;      Available Online: January 2015.