### Abstract

We observe a countable family of real valued sequences J_{p}, 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 q^{th} 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 language | English (US) |
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Pages (from-to) | 3022-3027 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 3 |

State | Published - Dec 1 1995 |

Event | Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA Duration: Dec 13 1995 → Dec 15 1995 |

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization