Dual approximation between optimal μ and optimal H controllers

Ciann-Dong Yang, Chia Yuan Chang, Fang Bo Yeh

Research output: Contribution to journalConference article


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 Fl(P, K), there exists a scalar frequency-shaping function W(s) such that the weighted H-optimization problem infK ∥W Fl(P, K)∥ is identical to the μ- optimization problem infK sup$-ω/μΔ(Fl(P, K))(jω); on the other hand, it is also shown that there exists a frequency-shaping function W*(s) such that the weighted μ-optimization problem infK(*) sup$-ω/μΔ(W*Fl(P, K*)) (jω) is identical to the H-optimization problem infK(*) ∥Fl (P, K*)∥. The frequency-shaping functions W(s), W*(s), and the optimal controllers Kopt(s), Kopt*(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 languageEnglish
Pages (from-to)2860-2864
Number of pages5
JournalProceedings of the American Control Conference
Publication statusPublished - 1995 Jan 1
EventProceedings of the 1995 American Control Conference. Part 1 (of 6) - Seattle, WA, USA
Duration: 1995 Jun 211995 Jun 23

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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