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

TL;DR

This paper introduces a sequential penalized convex relaxation method for solving bilinear matrix inequality problems in optimal control, demonstrating promising results on benchmark control design tasks.

Contribution

It extends previous work by developing a sequential scheme that improves feasibility and optimality in BMI problems for control synthesis.

Findings

Effective in designing H2 and Hinfinity controllers

Performs well on centralized and decentralized control problems

Outperforms existing methods on benchmark tests

Abstract

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.