Suboptimal control of bunches of trajectories of discrete deterministic automaton time-invariant systems

Abstract

The optimal control problem for discrete deterministic time-invariant automaton systems under parametric uncertainty is considered. The changes in the state (switching) of the system are described by a recurrence equation. The switching times and their number are not specified in advance—they are found by optimization. The initial state of the system is not known exactly. For this reason, the problems of finding the optimal on the average and the optimal guaranteeing (minimax) controls of bunches of trajectories are formulated. It is proposed to solve these problems using the separation principle, which assumes that the bunch is controlled using the control that is optimal for a specially chosen individual trajectory in the bunch. Generally, this control is suboptimal. Algorithms for the synthesis of suboptimal control of bunches are developed. It is proved that, in the linear-quadratic time-invariant problems, the suboptimal bunch control is optimal on the average or is the optimal minimax control, depending on the problem being solved.