On the Equivalence of Youla, System-Level, and Input–Output Parameterizations
On the Equivalence of Youla, System-Level, and Input–Output Parameterizations
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论Youla、系统级和输入输出参数化的等价性
DOI：
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发表时间：
2019
影响因子：
6.8
通讯作者：
M. Kamgarpour
中科院分区：
文献类型：
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作者：
Yang Zheng;Luca Furieri;A. Papachristodoulou;Na Li;M. Kamgarpour
内稳定控制器的凸参数化是许多控制器综合过程的基础。著名的Youla参数化依赖于系统的双素数分解，而最近的系统级参数化和输入输出参数化不需要双素数分解，而是一组可实现的闭环响应的相等约束。在本文中，我们展示了Youla、系统级和输入-输出参数化之间的显式仿射映射。这些仿射映射的两个直接含义是：1)在Youla、系统级或输入-输出参数中的任何凸问题都可以在这些框架中的任何一个框架中等价地和凸地表述，包括凸系统级综合；2)经典分布控制问题的二次不变条件是允许在优拉、系统级或输入-输出参数方面的等效凸重构的充分必要条件。
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.