Discrete stochastic system linear output control with respect to a quadratic criterion

Abstract

An optimization problem with the quality criterion that differs from the conventional one by some modifications is given. The state of the system is described by a second-order unobservable random sequence, while the observations are described by an optimizable noisy linear output. The fact that the unobservable state of the system is independent of the control is substantiated by interpreting the statement as the optimization problem for resource allocation for the system as opposed to the conventional statement that suggests controlling its state. A variant of the practical substantiation of the statement involved, i.e., optimizing operation of a software system, is proposed. A dynamic programming method is used to solve the problem. The optimal strategy is found as a linear combination of the output and predictions of the state up to the optimization horizon. Since the optimal strategy is computationally laborious, the possibility to simplify it and apply a locally optimal strategy is discussed.