Zubov's equation for state-constrained perturbed nonlinear systems

Titelangaben

Grüne, Lars ; Zidani, Hasnaa:
Zubov's equation for state-constrained perturbed nonlinear systems.
In: Mathematical Control and Related Fields. Bd. 5 (2015) Heft 1 . - S. 55-71.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2015.5.55

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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.