Structured state space realizations for SLS distributed controllers

In recent work the system level synthesis (SLS) paradigm has been shown to provide a truly scalable method for synthesizing distributed feedback controllers. Moreover, the resulting synthesis problem is convex. In this paper we provide minimal state space realizations for both the state and output feedback controllers. It is also shown that (for fixed n) the state dimension of the controllers grows linearly with FIR filter horizon length — in both cases, we show that if the underlying transfer matrices are structured, so is the corresponding state-space realization. For the H2 state feedback case a simple decomposition technique reduces the synthesis problem to solving a set of lower dimensional LQR problems that can be solved in parallel.

在最近的工作中，系统水平合成（SLS）范式已显示出一种真正可扩展的方法来综合分布式反馈控制器，而所得的合成问题是在本文中。如果基本转移的物质是结构化的，那么对H2状态反馈案例的相应状态空间也是一种简单的分解技术，可以将合成问题降低，以解决一组可以并行解决的较低尺寸LQR问题。