A Nonlinear SDP Approach to Fixed-Order Controller Synthesis and Comparison with Two Other Methods Applied to an Active Suspension System*

Abstract

The computation of optimal H ∞ controllers with a prescribed order is motivated by real-time implementation on systems with a very high sampling rate. In this paper, we present a nonlinear SDP approach to the H ∞ fixed-order synthesis problem. The algorithm is an extension of a primal predictor-corrector method to non-convex problems. To avoid wrong step directions the usual Newton steps in the corrector are replaced by a curved line-search. The predictor steps are based on Dikin elliposids of a “convexified” domain. The method converges, under mild conditions, to a point that satisfies the first-order necessary conditions. We derived conditions to check second-order optimality in terms of the original SDP problem. We compared the method with two other methods for fixed-order control: a posteriori reduction and the cone complementarity method. We computed for all three methods sixth-order controllers for a 27th order plant of an active suspension system. The interior point method computes a controller which has slightly larger closed-loop H ∞ -norm than the full order controller. Results of experiments show that the controller computed with the interior point method practically achieved the control objectives.