Universal Regulators in Linear-Quadratic Optimization Problems

Abstract

In this report we present a short survey and analysis of certain new infinite-horizon linear-quadratic optimization problems. They differ from well-known ones (see [1]–[5] and others) mainly in the assumption that there is no full information on the parameters of external disturbance and the output reference signal. It turns out that in certain such problems the optimal regulator is not unique and a special optimal regulator can be found that does not depend on unknown parameters. Therefore it can be used in this uncertain situation. We shall say that this regulator is universal in a given class of unknown parameters. The cases of existence of a universal regulator might seem to be very exceptional because such regulator solves a family of optimization problems simultaneously. But at least one such example is known very well in the control theory: in the linear-quadratic optimization problem without external disturbances the optimal regulator u = Kx does not depend on the initial state value x(0) = a. We will consider other similar and more complicated cases.