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

Abstract

This paper involves the innovative development of a symmetric Gauss-Seidel ADMM algorithm to solve the H-infinity guaranteed cost control problem. In the presence of parametric uncertainties, the H-infinity guaranteed cost control problem generally leads to the large-scale optimization. This is due to the exponential growth of the number of the extreme systems involved with respect to the number of parametric uncertainties. In this work, through a variant of the Youla-Kucera parameterization, the stabilizing controllers are parameterized in a convex set; yielding the outcome that the H-infinity 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. Significantly, this approach alleviates the often-times prohibitively heavy computational burden typical in many H-infinity 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 the attained effectiveness, the methodology thus evidently possesses extensive applicability in various important controller synthesis problems, such as decentralized control, sparse control, and output feedback control problems.

arXiv comment12 pages, 7 figures

References in corpus (3)

• Platooning of Connected Vehicles with Undirected Topologies: Robustness Analysis and Distributed H-infinity Controller Synthesis
• A Convex Information Relaxation for Constrained Decentralized Control Design Problems
• On Robust Stability and Performance with a Fixed-Order Controller Design for Uncertain Systems

Cited by in corpus (2)

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