Abstract
We consider a dynamical system simulating a switching device that changes its state finitely many times during operation. Changes of state (switchings) are described by a recurrent inclusion that corresponds to a representation of the system as a dynamic automaton with memory. The switching times and the number of switchings are not a priori known and are found by minimizing the functional. We find sufficient and necessary optimality conditions for such systems. We obtain an equation for synthesis of optimal trajectories. The optimality condition is illustrated by examples.
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