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.

Nadezhda Maltugueva, Programmer, Matrosov Institute for System Dynamics and Control Theory SB RAS, 134, Lermontov st., Irkutsk, 664033, Russian Federation, tel.: (3952) 45-30-37, e-mail: malt@icc.ru

Nikolay Pogodaev, Cand. Sci. (Phys.–Math.), Senior Research Scientist, Matrosov Institute for System Dynamics and Control Theory SB RAS, 134, Lermontov st., Irkutsk, 664033, Russian Federation, tel.: (3952) 45-30-52, e-mail: n.pogodaev@icc.ru

Olga Samsonyuk, Cand. Sci. (Phys.–Math.), Senior Research Scientist, Matrosov Institute for System Dynamics and Control Theory SB RAS, 134, Lermontov st., Irkutsk, 664033, Russian Federation, tel.: (3952)45-31-51, e-mail: samsonyuk.olga@gmail.com

Maltugueva N.S., Pogodaev N.I., Samsonyuk O.N. Optimization of Impulsive Control Systems with Intermediate State Constraints. The Bulletin of Irkutsk State University. Series Mathematics, 2021, vol. 35, pp. 18-33. https://doi.org/10.26516/1997-7670.2021.35.18

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