A Polynomial Chaos Approach to Robust H8 Static Output-Feedback Control With Bounded Truncation Error

• 成果类型: Article
• 署名作者: Wan, Yiming; Shen, Dongying E. E.; Lucia, Sergio; Findeisen, Rolf; Braatz, Richard D. D.
• 署名单位: Huazhong University of Science & Technology; Massachusetts Institute of Technology (MIT); Dortmund University of Technology; Technical University of Darmstadt
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3140275
• 发表日期: 2023
• 页码: 470-477
• 关键词: Control design; Control system synthesis; control theory; H infinity control; Linear matrix inequalities; optimal control; uncertain systems

摘要

article considers the H-infinity static output-feedback control for linear time-invariant uncertain systems with polynomial dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos theory, the control synthesis problem is solved using a high-dimensional expanded system, which characterizes stochastic state uncertainty propagation. A closed-loop polynomial chaos transformation is proposed to derive the closed-loop expanded system. The approach explicitly accounts for the closed-loop dynamics and preserves the L-2 induced gain, which results in smaller transformation errors compared to existing polynomial chaos transformations. The effect of using finite-degree polynomial chaos expansions is first captured by a norm-bounded linear differential inclusion, and then addressed by formulating a robust polynomial chaos based control synthesis problem. This proposed approach avoids the use of high-degree polynomial chaos expansions to alleviate the destabilizing effect of truncation errors, which significantly reduces computational complexity. A numerical example illustrates the effectiveness of the proposed approach.