Multi-objective H2/H-infinity-Optimal Control via Finite Dimensional Q-Parametrization and Linear Matrix Inequalities

H. Hindi, B. Hassibi, and S. Boyd

Proceedings of the American Control Conference, 5:3244-3249, June 1998.

The problem of multi-objective H2/H-infinity optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer. The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H2 and H-infinity norms. Suboptimal solutions are computed using finite dimensional Q-parametrization. The objective value of the suboptimal Q's converges to the true optimum as the dimension of Q is increased. State space representations are presented which are the analog of those given by Khargonekar and Rotea for the H2 case. A simple example computed using FIR (Finite Impulse Response) Q's is presented.