Dynamic systems and optimal control

Optimization of impulsive control systems with intermediate state constraints

N. S. Maltugueva^a, N. I. Pogodaev^ab, O. N. Samsonyuk<sup>a

a</sup> 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.

UDC: 517.977.5

MSC: 93C10, 93C30

Received: 02.10.2020

Language: English

DOI: 10.26516/1997-7670.2021.35.18

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