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

Mikhail Gomoyunov () and Dmitriy Serkov ()
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Mikhail Gomoyunov: Ural Branch of Russian Academy of Sciences
Dmitriy Serkov: Ural Branch of Russian Academy of Sciences

Dynamic Games and Applications, 2019, vol. 9, issue 3, No 8, 700-723

Abstract: 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.

Keywords: Control problem; Disturbances; Functional constraint; Optimal guaranteed result; Optimal strategy; Reconstruction; Numerical method (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13235-018-0279-1

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