On Symmetric Gauss-Seidel ADMM Algorithm for H∞ Guaranteed Cost Control with Convex Parameterization

Abstract

This paper involves the innovative development of a symmetric Gauss-Seidel ADMM algorithm to solve the H∞ guaranteed cost control problem. Through a variant of the Youla-Kucera parameterization, the stabilizing controllers are parameterized in a convex set; yielding the outcome that the H∞ guaranteed cost control problem is converted to a convex optimization problem. Based on an appropriate re-formulation using the Schur complement, it then renders possible the use of the ADMM algorithm with symmetric Gauss-Seidel backward and forward sweeps. This approach alleviates the often-times prohibitively heavy computational burden typical in many H∞ optimization problems while exhibiting good convergence guarantees, which is particularly essential for the related large-scale optimization procedures involved. With this approach, the desired robust stability is ensured, and the disturbance attenuation is maintained at the minimum level in the presence of parametric uncertainties. Rather importantly too, with these attained effectiveness, the methodology thus evidently possesses extensive applicability in various important controller synthesis problems, such as decentralized control, sparse control, output feedback control problems, etc.