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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.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    M. I. Gusev

  2. Ural Federal University, Yekaterinburg, 620000, Russia

    M. I. Gusev

Authors
  1. M. I. Gusev
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Correspondence to M. I. Gusev.

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Original Russian Text © M.I.Gusev, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 2.

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Gusev, M.I. On the Existence of a Lipschitz Feedback Control in a Control Problem with State Constraints. Proc. Steklov Inst. Math. 299 (Suppl 1), 61–67 (2017). https://doi.org/10.1134/S0081543817090085

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  • DOI: https://doi.org/10.1134/S0081543817090085

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