### 摘要

The main purpose of this paper is to solve the dual approximation problem: approximation of optimal μ controllers by a sequence of fixed-order optimal H_{∞} controllers, and the dual approximation of optimal H_{∞} controllers by a sequence of fixed-order optimal μ controllers. It is shown analytically that for a control system described by the linear fractional transformation F_{l}(P, K), there exists a scalar frequency-shaping function W(s) such that the weighted H_{∞}-optimization problem inf_{K} ∥W F_{l}(P, K)∥_{∞} is identical to the μ- optimization problem inf_{K} sup$-ω/μΔ(F_{l}(P, K))(jω); on the other hand, it is also shown that there exists a frequency-shaping function W^{*}(s) such that the weighted μ-optimization problem inf_{K(*)} sup$-ω/μΔ(W^{*}F_{l}(P, K^{*})) (jω) is identical to the H_{∞}-optimization problem inf_{K(*)} ∥F_{l} (P, K^{*})∥_{∞}. The frequency-shaping functions W(s), W^{*}(s), and the optimal controllers K_{opt}(s), K_{opt}^{*}(s) are characterized explicitly in terms of a dual pair of minimizing sequences, and are solved numerically by a dual pair of iteration algorithms.

原文 | English |
---|---|

頁（從 - 到） | 2860-2864 |

頁數 | 5 |

期刊 | Proceedings of the American Control Conference |

卷 | 4 |

出版狀態 | Published - 1995 一月 1 |

事件 | Proceedings of the 1995 American Control Conference. Part 1 (of 6) - Seattle, WA, USA 持續時間: 1995 六月 21 → 1995 六月 23 |

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

## 指紋 深入研究「Dual approximation between optimal μ and optimal H<sub>∞</sub> controllers」主題。共同形成了獨特的指紋。

## 引用此

_{∞}controllers.

*Proceedings of the American Control Conference*,

*4*, 2860-2864.