Robust optimal parametric LQ control with a guaranteed cost bound and applications

Abstract

For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closed-loop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system via a parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem is referred to as ‘robust optimal parametric LQ control with a guaranteed cost bound’ and is addressed in this work. A new design method is proposed to find an optimal controller for simultaneously guaranteeing robust stability and performance over a specified range of parameter variations. The results presented generalize some previous work in this area. A versatile numerical algorithm is also given for computing the robust optimal gains. The usefulness of the design method is demonstrated by numerical examples and a design of the robust control of a VTOL helico...