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.
|Number of pages||5|
|Journal||Proceedings of the American Control Conference|
|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