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**On a solution of a guarantee optimization problem under the functional constraints on the disturbance.**
*(English)*
Zbl 1431.93043

Summary: 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.

### MSC:

93C73 | Perturbations in control/observation systems |

93C15 | Control/observation systems governed by ordinary differential equations |

49J15 | Existence theories for optimal control problems involving ordinary differential equations |

91A80 | Applications of game theory |

### Keywords:

control problem; disturbances; functional constraint; optimal guaranteed result; optimal strategy; reconstruction; numerical method
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\textit{M. Gomoyunov} and \textit{D. Serkov}, Dyn. Games Appl. 9, No. 3, 700--723 (2019; Zbl 1431.93043)

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### References:

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