Optimal control of linear plants with random parameters

The subject of this paper is the optimal control of linear plants whose coefficients and whose reference signals are random processes. The discrete-time as well as the continuous-time problems are treated and some fairly deep-seated distinctions between the two are pointed out. Special emphasis is placed on control over long periods of time. A set of assumptions is laid down under which the transition to infinitely long periods of operation is tractable. It is shown that a discrete-time plant is controllable, in the sense that the rate of the mean-squared error remains finite, only when certain necessary and sufficient conditions are fulfilled by the statistics of the plant parameters.