Model and controller selection policies based on output prediction errors

Based an observations of the past inputs and outputs of an unknown system Sigma, a countable set of predictors, O-p, p is an element of P, is used to predict the system output sequence. Using performance measures derived from the resultant prediction errors, a decision rule is to be designed to select a p is an element of p at each time k. We study the structure and memory requirements of decision rules that converge to some q is an element of p such that the qth prediction error sequence has desirable properties, e.g., is suitably bounded or converges to zero. In a very general setting we give a positive result that there exist stationary decision rules with countable memory that converge (in finite time) to a ''good'' predictor. These decision rules are robust in a sense made precise in the paper, in addition, we demonstrate that there does not exist a decision rule with finite memory that has this property, This type of problem arises in a variety of contexts, but one of particular interest is the following. Based on the decision rule's selection at time k, a controller for the system Sigma is chosen from a family Gamma(p).p is an element of P of predesigned control systems. We show that for certain multi-input/multi-output linear systems the resultant closed-loop controlled system is stable and can asymptotically track an exogenous reference input.