Self-tuning regulators for a class of multivariable systems

Abstract

Control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed. A multivariable minimum variance strategy is first presented. This gives a generalization of the minimum variance strategy for single-input single-output systems. A multivariable self-tuning regulator based on the minimum variance strategy is then proposed. It uses a recursive least squares estimator and a linear controller obtained directly from the current estimates. The asymptotic properties of the algorithm are discussed. If the estimated parameters converge, the resulting controller will under certain conditions give the minimum variance strategy. The analysis also gives insight into the case when several single-input single-output self-tuning regulators are operating in cascade mode.