### Abstract

In adaptive control, it is often useful to distinguish between transient and asymptotic performance. In this paper, we formulate a notion of asymptotic performance for an H_{∞} adaptive control problem, and consider the problem in the simple case where the unknown plant is one of a finite number of known, possible models. We consider two plant cases: a) the plants are simply static nonlinear functions, and b) the plants are linear and time-invariant. Our main result is that, for both cases, the optimal asymptotic H_{∞} performance is no better than the optimal performance in the transient phase. We conclude that increased input-output data does not improve the achievable H_{∞} performance. Instead, parametric uncertainty results in a persistent performance degradation, and this uncertainty cannot be resolved, even with infinite data.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Editors | Anon |

Pages | 3755-3759 |

Number of pages | 5 |

State | Published - 1996 |

Event | Proceedings of the 35th IEEE Conference on Decision and Control. Part 4 (of 4) - Kobe, Jpn Duration: Dec 11 1996 → Dec 13 1996 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 4 |

ISSN (Print) | 0191-2216 |

### Other

Other | Proceedings of the 35th IEEE Conference on Decision and Control. Part 4 (of 4) |
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City | Kobe, Jpn |

Period | 12/11/96 → 12/13/96 |

### ASJC Scopus subject areas

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

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## Cite this

_{∞}control. In Anon (Ed.),

*Proceedings of the IEEE Conference on Decision and Control*(pp. 3755-3759). (Proceedings of the IEEE Conference on Decision and Control; Vol. 4).