Model and controller selection policies based on output prediction errors

Based on observations of the past inputs and outputs of an unknown system /spl Sigma/, a countable set of predictors, O/sub p/, p/spl isin/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/spl isin/P at each time /spl kappa/. We study the structure and memory requirements of decision rules that converge to some q/spl isin/P such that the qth prediction error sequence has desirable properties. In a very general setting we give a positive result that there exist stationary derision rules with countable memory that converge 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. Based on the decision rule's selection at time /spl kappa/, a controller for the system /spl Sigma/ is chosen from a family /spl Gamma//sub p//spl isin/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.