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This paper involves the innovative development of a symmetric Gauss-SeidelADMM algorithm to solve the H-infinity guaranteed cost control problem. In thepresence of parametric uncertainties, the H-infinity guaranteed cost controlproblem generally leads to the large-scale optimization. This is due to theexponential growth of the number of the extreme systems involved with respectto the number of parametric uncertainties. In this work, through a variant ofthe Youla-Kucera parameterization, the stabilizing controllers areparameterized in a convex set; yielding the outcome that the H-infinityguaranteed cost control problem is converted to a convex optimization problem.Based on an appropriate re-formulation using the Schur complement, it thenrenders possible the use of the ADMM algorithm with symmetric Gauss-Seidelbackward and forward sweeps. Significantly, this approach alleviates theoften-times prohibitively heavy computational burden typical in many H-infinityoptimization problems while exhibiting good convergence guarantees, which isparticularly essential for the related large-scale optimization proceduresinvolved. With this approach, the desired robust stability is ensured, and thedisturbance attenuation is maintained at the minimum level in the presence ofparametric uncertainties. Rather importantly too, with the attainedeffectiveness, the methodology thus evidently possesses extensive applicabilityin various important controller synthesis problems, such as decentralizedcontrol, sparse control, and output feedback control problems.

On Symmetric Gauss-Seidel ADMM Algorithm for $\mathcal{H}_\infty$ Guaranteed Cost Control with Convex Parameterization