## Abstract

This paper shows how H^{∞} near-optimal finite-dimensional compensators may be designed for linear time invariant (LTI) infinite-dimensional plants subject to convex constraints. The infinite-dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity H^{∞} optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite-dimensional optimization problem to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed-sensitivity H^{∞} control system design problems, subgradient concepts are used to directly accommodate timedomain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. Illustrative examples for thermal, structural, and aircraft systems are provided.

Original language | English (US) |
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Title of host publication | Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1209-1214 |

Number of pages | 6 |

ISBN (Print) | 1424401712, 9781424401710 |

State | Published - 2006 |

Event | 45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: Dec 13 2006 → Dec 15 2006 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0743-1546 |

ISSN (Electronic) | 2576-2370 |

### Other

Other | 45th IEEE Conference on Decision and Control 2006, CDC |
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Country/Territory | United States |

City | San Diego, CA |

Period | 12/13/06 → 12/15/06 |

## ASJC Scopus subject areas

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

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