Model and controller selection policies based on output prediction errors

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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 ε 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 ε P at each time k. We study the structure and memory requirements of decision rules that converge to some q ε 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 Σ is chosen from a family Γp, p ε 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.

Original languageEnglish (US)
Pages (from-to)1594-1604
Number of pages11
JournalIEEE Transactions on Automatic Control
Volume41
Issue number11
DOIs
StatePublished - Dec 1 1996

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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