Convex Relaxation of Bilinear Matrix Inequalities Part II: Applications to Optimal Control Synthesis

The first part of this paper proposed a family of penalized convex relaxations for solving optimization problems with bilinear matrix inequality (BMI) constraints. In this part, we generalize our approach to a sequential scheme which starts from an arbitrary initial point (feasible or infeasible) and solves a sequence of penalized convex relaxations in order to find feasible and near-optimal solutions for BMI optimization problems. We evaluate the performance of the proposed method on the H2 and Hinfinity optimal controller design problems with both centralized and decentralized structures. The experimental results based on a variety of benchmark control plants demonstrate the promising performance of the proposed approach in comparison with the existing methods.