Geodesic
Optimization of impulsive control systems with intermediate state constraints
The Bulletin of Irkutsk State University. Series Mathematics, Tome 35 (2021), pp. 18-33

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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. 
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     author = {N. S. Maltugueva and N. I. Pogodaev and O. N. Samsonyuk},
     title = {Optimization of impulsive control systems with intermediate state constraints},
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     pages = {18--33},
     publisher = {mathdoc},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_35_a1/}
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N. S. Maltugueva; N. I. Pogodaev; O. N. Samsonyuk. Optimization of impulsive control systems with intermediate state constraints. The Bulletin of Irkutsk State University. Series Mathematics, Tome 35 (2021), pp. 18-33. http://geodesic.mathdoc.fr/item/IIGUM_2021_35_a1/