Synthesis of optimal H∞ controllers via LQG-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 flat frequency response of the largest singular value. The weighted H₂ optimization technique used in LQG/LTR is exploited in the loop shaping procedures to generate a sequence of H₂ controllers converging to the optimal H_∞ controller. The resulting optimal H_∞ controller not only has the inherent robust property due to H_∞ criterion but also possesses the nice H₂ control structure, being easy to compute and implement. A flight control example is demonstrated to show that the numerical accuracy of the present LQG-based H_∞ synthesis is comparable to the conventional H_∞ approach, i.e. γ-iteration