Optimal and suboptimal control over bunches of trajectories of automaton-type deterministic systems

Abstract

The problem of optimal control of automatic deterministic discrete systems in conditions of parametric uncertainty is considered. The state change (switchover) of a system is described by a recurrent equation in which instant multiple switchovers are admitted. The times and the number of switchovers are not specified in advance—they are found as a result of optimization of a functional. The initial state of the system is not known exactly, but the set of possible initial states is known; therefore, problems of average optimal control and guaranteed optimal control of bunches of trajectories are formulated. For solving these problems, it is suggested to use the principle of separation: namely, to control the bunch of trajectories by applying a control optimal for one specially chosen trajectory of the bunch. The resulting control of the bunch is suboptimal, but it may be satisfactory in practice. On the basis of sufficient conditions for optimality of a full-feedback control, an algorithm for constructing a suboptimal control in conditions of uncertainty is developed. Counterexamples of linear–quadratic problems of control of automaton-type systems in which the principle of separation fails are presented.