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Necessary optimality conditions for switched systems. (English. Russian original) Zbl 1387.49036

J. Comput. Syst. Sci. Int. 55, No. 5, 712-724 (2016); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upr. 2016, No. 5, 34-46 (2016).
Summary: A dynamic system that models the operation of a switching device (switch) is considered. During the operation, the system changes its state a finite number of times. The change of state (switching) is described by a recurrent inclusion, which corresponds to the representation of the switch by a dynamic finite state machine with memory; instantaneous multiple switchings are admitted. The instants of time at which switchings are made and the number of switchings are not given in advance. They are found by optimizing a functional in which the number of switchings and the cost of each of them are taken into account. Necessary optimality conditions for such systems are proved. Different versions of the optimality conditions for different types of constraints are given. In particular, under additional convexity conditions, conditions that are similar to the maximum principle for discrete systems are obtained. The application of the optimality conditions is illustrated by examples.

MSC:

49K21 Optimality conditions for problems involving relations other than differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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