Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 66, Issue 1, Pages 413-420Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2020.2979785
Keywords
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
Funding
- NSF [1553407]
- AFOSR
- ONR
- ERC
- EPSRC [EP/M002454/1]
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [1553407] Funding Source: National Science Foundation
- EPSRC [EP/M002454/1] Funding Source: UKRI
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The article presents explicit affine mappings among Youla, system-level, and input-output parameterizations, and two direct implications of these affine mappings.
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.
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