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Synthesis of an Optimal System with Stable Sliding Modes

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Abstract

A method for synthesizing an optimal control that ensures the existence and stability of sliding modes for a system of nonlinear ordinary differential equations is proposed. This method uses an auxiliary optimal control problem. The solution gives a control in analytical form. It is proved that the trivial solution of the closed-loop system is Lyapunov stable. Application of the proposed method to linear and quasi-linear systems of equations is demonstrated, and an illustrative example is discussed.

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Authors and Affiliations

  1. Far Eastern Federal University, 690922, Vladivostok, Russia

    L. T. Ashchepkov

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  1. L. T. Ashchepkov
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Correspondence to L. T. Ashchepkov.

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The author declares that he has no conflicts of interest.

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Translated by A. Klimontovich

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Ashchepkov, L.T. Synthesis of an Optimal System with Stable Sliding Modes. Comput. Math. and Math. Phys. 63, 743–750 (2023). https://doi.org/10.1134/S0965542523050044

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  • DOI: https://doi.org/10.1134/S0965542523050044

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