Fitting controllers to data: the MIMO case

The problem of optimally fitting controllers to data is examined for the identification of a controller from a given class of MIMO controllers used in model reference adaptive control. The problem of identifying a MIMO controller from this class is formulated. This formulation leads to an optimization problem where a best 2 nm/sup 2/ x m matrix of parameters is looked for. It is proved that the solution to this problem can be given in terms of the solution of an optimization problem where a best 2 nm/sup 2/ /spl times/ 1 vector of parameters is looked for, which has already been solved for the SISO case. Simulations are provided for an example which has appeared a few times in the model reference adaptive control literature. The formulation and solution of this problem illustrates a unifying link between the design of model reference adaptive control for SISO and MIMO linear systems.