### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 2860-2864 |

Number of pages | 5 |

Journal | Proceedings of the American Control Conference |

Volume | 4 |

Publication status | Published - 1995 Jan 1 |

Event | Proceedings of the 1995 American Control Conference. Part 1 (of 6) - Seattle, WA, USA Duration: 1995 Jun 21 → 1995 Jun 23 |

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

## Fingerprint Dive into the research topics of 'Dual approximation between optimal μ and optimal H<sub>∞</sub> controllers'. Together they form a unique fingerprint.

## Cite this

_{∞}controllers.

*Proceedings of the American Control Conference*,

*4*, 2860-2864.