Synthesis of optimal H/sub ∞/ controllers via LQG-based loop shaping design

Abstract

Synthesis of optimal H/sub /spl infin// 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 H/sub 2/ optimization technique used in LQG/LTR is exploited in the loop shaping procedures to generate a sequence of H/sub 2/ controllers converging to the optimal H/sub /spl infin// controller. The resulting optimal H/sub /spl infin// controller not only has the inherent robust property due to H/sub /spl infin// criterion but also possesses the nice H/sub 2/ 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/sub /spl infin// synthesis is comparable to the conventional H/sub /spl infin// approach, i.e. /spl gamma/-iteration.