INVARIANCE PROPERTY WITH APPLICATION TO SOLVING CONTROL PROBLEMS

V. N. Ushakov (), S. A. Brykalov (), A. R. Matviychuk () and A. V. Ushakov ()
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V. N. Ushakov: Department of Dynamical Systems, Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences and Ural Federal University, 16, S.Kovalevskaja street, Ekaterinburg, 620990, Russia
S. A. Brykalov: Department of Dynamical Systems, Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences and Ural Federal University, 16, S.Kovalevskaja street, Ekaterinburg, 620990, Russia
A. R. Matviychuk: Department of Dynamical Systems, Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences and Ural Federal University, 16, S.Kovalevskaja street, Ekaterinburg, 620990, Russia
A. V. Ushakov: Department of Dynamical Systems, Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences and Ural Federal University, 16, S.Kovalevskaja street, Ekaterinburg, 620990, Russia

International Game Theory Review (IGTR), 2014, vol. 16, issue 02, 1-19

Abstract: We consider controlled systems and differential inclusions on a bounded time interval. The investigated problem brings the controlled system to a fixed compact target set in the phase space at a finite time moment. It is known that integral funnels of controlled systems and differential inclusions satisfy the invariance property. We discuss application of the invariance property to constructing approximations to integral funnels. Examples of nonlinear controlled systems are considered in which the proposed algorithm is realized.

Keywords: Controlled system; attainability set; integral funnels; invariance; 34K35; 49K15; 49K24; 93C10 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0219198914400131

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