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On the Existence of a Lipschitz Feedback Control in a Control Problem with State Constraints

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Abstract

We consider a nonlinear control system with state constraints given as a solution set for a finite system of nonlinear inequalities. The problem of constructing a feedback control that ensures the viability of trajectories of the closed system in a small neighborhood of the boundary of the state constraints is studied. Under some assumptions, the existence of a feedback control in the form of a Lipschitz function of the state of the system is proved.

Keywords

state constraints feedback control viability problem invariance. 

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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsUral Branch of the Russian Academy of SciencesYekaterinburgRussia
  2. 2.Ural Federal UniversityYekaterinburgRussia

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