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Impulse controls in models of hybrid systems

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Abstract

We consider a mathematical model of a hybrid system in which the continuous dynamics induced at each instant of time by a certain system of differential equations from a given finite family is alternated with discrete operations sending commands either for an instantaneous switching from one system to another, or for an instantaneous reset from online coordinates to other coordinates, or for both actions together. We present a description of a hybrid system via systems with impulses. We suggest a new scheme, which permits one to reduce the problem of synthesis of controls for a hybrid system to an impulse control problem. The aim of the present paper is to find a control containing both ordinary components (that are not generalized functions) and higher-order generalized functions.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. B. Kurzhanski & P. A. Tochilin

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  1. A. B. Kurzhanski
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  2. P. A. Tochilin
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Original Russian Text © A.B. Kurzhanski, P.A. Tochilin, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 5, pp. 716–727.

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Kurzhanski, A.B., Tochilin, P.A. Impulse controls in models of hybrid systems. Diff Equat 45, 731–742 (2009). https://doi.org/10.1134/S0012266109050127

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  • DOI: https://doi.org/10.1134/S0012266109050127

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