On the existence and memory requirements of convergent on-line decision rules

Research output: Contribution to journalConference articlepeer-review


We observe a countable family of real valued sequences Jp, p ε P, and we want to design a decision rule that at each time k selects a parameter p ε P based on the past observations in such a way that the decisions converge to some q ε P with the qth data sequence having desirable properties, e.g., is suitably bounded or converges to zero. In a general setting we give a positive result that there exist decision rules with countable memory that converge (in finite time) to a 'correct selection'. 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 such as on-line model selection and on-line controller selection.

Original languageEnglish (US)
Pages (from-to)3022-3027
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 1995
EventProceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA
Duration: Dec 13 1995Dec 15 1995

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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