Zubov's equation for state-constrained perturbed nonlinear systems

Lars Grüne 1 Hasnaa Zidani 2, 3
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : The paper gives a characterization of the uniform robust domain of attraction for a nite 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 in nite 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.
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Lars Grüne, Hasnaa Zidani. Zubov's equation for state-constrained perturbed nonlinear systems. Mathematical Control and Related Fields, AIMS, 2015, 5 (1), pp.55-71. ⟨10.3934/mcrf.2015.5.55⟩. ⟨hal-00931028⟩

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