Abstract
A dynamical system simulating the operation of a switching device (switch) is considered. When functioning, the system changes its state a finite number of times. The change in the state (switching) is described by a recurrent activation when the switch is represented as a dynamic automaton with memory and instantaneous multiple switchings. The times at which switchings occur and their number are not prescribed. These values are determined from the optimization of a functional that calculates the number and cost of switchings. We have proved the sufficient conditions of the optimality of these systems and developed a method for synthesizing optimum switches. This method builds a family of auxiliary functions (conditional cost functions and conditional positional controls) that serve to form a cost function (a Hamilton--Jacobi--Bellman function) and an optimal scheme of the switch. The application of this method is illustrated by some examples.
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