Synthesis of optimal H_∞ controllers via H₂-based loop-shaping design

Synthesis of optimal H_∞ controllers is formulated as a loop-shaping problem where the desired closed-loop shape to be pursued is a uniform frequency response of the largest singular value. The weighted H₂ optimization technique used in the linear quadratic Gaussian design with loop transfer recovery is exploited in the loop-shaping procedures to generate a sequence of H₂ controllers converging to the optimal H₂, controller. The resulting optimal H_∞ controller not only has the inherent robust property due to H_∞ criterion but also possesses the nice H_∞ control structure, being easy to compute and implement. A fighter example and a large space structure example are demonstrated to show that the numerical accuracy of the present H₂-based H_∞ synthesis is comparable to the conventional H_∞ approach, i.e., γ-iteration, but with reduced computational efforts.