Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM

• 成果类型: Article
• 署名作者: Ma, Jun; Cheng, Zilong; Zhang, Xiaoxue; Tomizuka, Masayoshi; Lee, Tong Heng
• 署名单位: National University of Singapore; University of California System; University of California Berkeley; National University of Singapore
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3052768
• 发表日期: 2021
• 页码: 5554-5560
• 关键词: Decentralized control; optimization; uncertain systems; Symmetric matrices; Aerospace electronics; linear programming; Robustness; Augmented Lagrangian method; Convex Optimization; convex restriction; decentralized control; optimal control; parameter space; parameter uncertainties

摘要

The H-2-guaranteed cost decentralized control problem is investigated in this article. More specifically, on the basis of an appropriate H-2 reformulation that we put in place, the optimal control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing decentralized controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symmetric Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which attains high computational effectiveness. A comprehensive analysis is given on the application of the approach in solving the optimal decentralized control problem; and subsequently, the preserved decentralized structure, robust stability, and robust performance are all suitably guaranteed with the proposed methodology. Furthermore, an illustrative example is presented to demonstrate the effectiveness of the proposed optimization approach.