The role of the interactor matrix in multivariable stochastic adaptive control

This paper is concerned with the extension of the well-known minimum variance control strategy to the multi-input-multi-output case. It is shown that this extension is straightforward when the system interactor matrix is diagonal but presents some unexpected difficulties in the general case. We develop a suitable stochastic controller for the general case as a logical extension of the single input algorithm. We also explore the properties of the algorithm in detail. We also address the question of adaptive control of multivariable stochastic systems and investigate one possible strategy for overcoming the requirement of knowing the system interactor matrix a priori.