Regulation of Incompletely Identified Linear Systems

This paper is concerned with regulation of linear systems disturbed by stationary Gaussian processes. Neither the noise nor system characteristics are assumed to be known a priori, but the input and output signals can be observed for the purpose of identification. The problem is to find a feedback law, a linear function of finitely many past observations, which minimizes an appropriate objective function measuring the goodness of the regulation. Precise conditions under which the problem can be solved with a stable control law are stated, and an algorithm for finding the solution with arbitrary accuracy is given