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Dynamic systems and optimal control
Optimization of impulsive control systems with intermediate state constraints
N. S. Maltuguevaa, N. I. Pogodaevab, O. N. Samsonyuka a Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russian Federation
b Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russian
Federation
Abstract:
In this paper, we consider an optimal impulsive control problem with intermediate state constraints. The peculiarity of the problem consists in a non-standard way of specifying of intermediate constraints. So the constraints must be satisfied for at least one selection of a set-valued solution to the impulsive control system. We prove a theorem for the existence of an optimal control and propose the reduction procedure that transforms the initial optimal control problem with intermediate constraints into a hybrid problem with control parameters. This hybrid problem gives an equivalent description of the optimal impulsive control problem. We discuss a numerical algorithm based on a direct collocation method and give a schema to the corresponding numerical calculations for a test example.
Keywords:
impulsive control, trajectory of bounded variation, intermediate state constraints, numerical method.
Received: 02.10.2020
Citation:
N. S. Maltugueva, N. I. Pogodaev, O. N. Samsonyuk, “Optimization of impulsive control systems with intermediate state constraints”, Bulletin of Irkutsk State University. Series Mathematics, 35 (2021), 18–33
Linking options:
https://www.mathnet.ru/eng/iigum441 https://www.mathnet.ru/eng/iigum/v35/p18
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Abstract page: | 108 | Full-text PDF : | 60 | References: | 13 |
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