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On a Solution of a Guarantee Optimization Problem Under the Functional Constraints on the Disturbance

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Abstract

The paper deals with a control problem for a dynamical system under disturbances. A motion of the system is considered on a finite interval of time and described by a nonlinear ordinary differential equation. The control is aimed at minimization of a given quality index. In addition to geometric constraints on the control and disturbance, it is supposed that the disturbance satisfies a compact functional constraint. Namely, all disturbance realizations that can happen in the system belong to some unknown set that is compact in the space \(L_1\). Within the game-theoretical approach, the problem of optimizing the guaranteed result of the control is studied. For solving this problem, we propose a new construction of the optimal control strategy. In the linear-convex case, this strategy can be numerically realized on the basis of the upper convex hulls method. Examples are considered. Results of numerical simulations are given.

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Acknowledgements

We thank the referees for their careful reading and their remarks that allowed us to improve the paper.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya Str., 16, Ekaterinburg, Russia

    Mikhail Gomoyunov & Dmitriy Serkov

  2. Ural Federal University, Mira Str., 32, Ekaterinburg, Russia

    Mikhail Gomoyunov & Dmitriy Serkov

Authors
  1. Mikhail Gomoyunov
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  2. Dmitriy Serkov
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Corresponding author

Correspondence to Mikhail Gomoyunov.

Additional information

This work was supported by the Integrated Program for Fundamental Research of the Ural Branch of the Russian Academy of Sciences (Project No. 18-1-1-10).

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Gomoyunov, M., Serkov, D. On a Solution of a Guarantee Optimization Problem Under the Functional Constraints on the Disturbance. Dyn Games Appl 9, 700–723 (2019). https://doi.org/10.1007/s13235-018-0279-1

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  • DOI: https://doi.org/10.1007/s13235-018-0279-1

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