Model and controller selection policies based on output predictionerrors |
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Authors: | Kulkarni SR Ramadge PJ |
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Affiliation: | Dept. of Electr. Eng., Princeton Univ., NJ; |
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Abstract: | Based on observations of the past inputs and outputs of an unknown system Σ, a countable set of predictors, Op, p∈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∈P at each time κ. We study the structure and memory requirements of decision rules that converge to some q∈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 κ, a controller for the system Σ is chosen from a family Γp ∈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 |
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