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Zubov's equation for state-constrained perturbed nonlinear systems

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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Submitted on : Tuesday, January 14, 2014 - 6:05:20 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:05 PM
Long-term archiving on: : Tuesday, April 15, 2014 - 4:28:23 PM


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Lars Grüne, Hasnaa Zidani. Zubov's equation for state-constrained perturbed nonlinear systems. Mathematical Control and Related Fields, 2015, 5 (1), pp.55-71. ⟨10.3934/mcrf.2015.5.55⟩. ⟨hal-00931028⟩



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