Fitting controllers to data

The problem of optimally fitting controllers to data is formulated and solved in the behavioral framework of Willems (1991) expanded to accommodate partial information about signals. This formulation is applied to the case in which the class of controllers considered is the same as the one used in model reference adaptive control problem and in which we minimize the induced norm of the control error. The solution to this problem, besides illustrating an use of the saying "let the data speak" to its extremes, gives a robustness-oriented perspective on model reference adaptive control.