Sufficient optimality conditions for discrete automaton-type systems

A discrete system that models the operation of a dynamic automaton with memory is considered. In distinction from the ordinary models of discrete systems, in which the states are changed (switched) at prescribed instants of time, automaton-type systems may change their states at arbitrary instants. Furthermore, the choice of the instants when the automaton “fires” is a control resource and it is subject to optimization. Sufficient optimality conditions for such systems under a limited or unlimited number of switchings are proved. Equations for the synthesis of the optimal closed-loop control are derived. Application of the optimality conditions is illustrated by examples.