Abstract

In this paper, synthesis of the optimal H∞ controllers is formulated as a loop-shaping problem where the desired loop shapc to be pursued is a flat frequency response of the largest singular value. The paper contains three parts. (1) H2-based loop shaping design: Weighted H2 optimization used in LQG/LTR is exploited in the loop shaping procedures to generate a sequence of H2 controllers converging to the optimal H∞ controller. (2) Lp-based loop shaping design: Besides H2-based loop shaping design, we establish a more general loop shaping philosophy based on Lp optimization. It is shown that H∞-optimization problem is equivalent to weighted Lp-optimization problem with p < 00, and any type of optimal Lp controllers including L1 and H2 can be properly shaped to become an optimal H∞ controller. (3)μ-based loop shaping design : The generalized loop shaping design presented here is not limited to norm-based criterion. Loop shaping design based on structured singular value is proposed to synthesize optimal H∞ controllers.

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