On the Equivalence of Youla, System-Level, and Input-Output Parameterizations

• 成果类型: Article
• 署名作者: Zheng, Yang; Furieri, Luca; Papachristodoulou, Antonis; Li, Na; Kamgarpour, Maryam
• 署名单位: Harvard University; Harvard University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oxford
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2979785
• 发表日期: 2021
• 页码: 413-420
• 关键词: Linear systems; optimal control; ELECTRONIC MAIL; decentralized control; Adaptive control; Closed loop systems; Task analysis; Quadratic invariance (QI); stabilizing controller; system-level synthesis (SLS); Youla parameterization

摘要

A convex parameterization of internally stabilizing controllers is fundamental for many controller synthesis procedures. The celebrated Youla parameterization relies on a doubly coprime factorization of the system, while the recent system-level and input-output parametrizations require no doubly coprime factorization, but a set of equality constraints for achievable closed-loop responses. In this article, we present explicit affine mappings among Youla, system-level, and input-output parameterizations. Two direct implications of these affine mappings are: 1) any convex problem in the Youla, system-level, or input-output parameters can be equivalently and convexly formulated in any other one of these frameworks, including the convex system-level synthesis; 2) the condition of quadratic invariance is sufficient and necessary for the classical distributed control problem to admit an equivalent convex reformulation in terms of either Youla, system-level, or input-output parameters.