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

Author

Listed:
  • Mikhail Gomoyunov

    (Ural Branch of Russian Academy of Sciences
    Ural Federal University)

  • Dmitriy Serkov

    (Ural Branch of Russian Academy of Sciences
    Ural Federal University)

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 $$L_1$$ 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.

Suggested Citation

  • Mikhail Gomoyunov & Dmitriy Serkov, 2019. "On a Solution of a Guarantee Optimization Problem Under the Functional Constraints on the Disturbance," Dynamic Games and Applications, Springer, vol. 9(3), pages 700-723, September.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:3:d:10.1007_s13235-018-0279-1
    DOI: 10.1007/s13235-018-0279-1
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    References listed on IDEAS

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    1. Nikolai Lukoyanov & Mikhail Gomoyunov, 2019. "Differential Games on Minmax of the Positional Quality Index," Dynamic Games and Applications, Springer, vol. 9(3), pages 780-799, September.
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