Optimal and suboptimal control of bundle of trajectories of deterministic logical-dynamical systems

The optimal control problem for deterministic logical-dynamical systems, with their continuous part described by differential equations and their discrete part described by recurrence equations, which simulate the operation of an automaton with memory, is considered. Algorithms for constructing the suboptimal guaranteeing and suboptimal on average controls under uncertainty are proposed based on sufficient optimality conditions for complete feedback control. It is shown that for linear logical-dynamical systems with the quadratic control criterion, the optimal open-loop control of the bundle coincides with the optimal control of its trajectory, i.e., the suboptimal control is optimal. Examples are given to illustrate the way to apply optimality and suboptimality conditions.