论文标题
对具有稀疏性约束的空间分布控制器的闭环的明确参数化
An Explicit Parametrization of Closed Loops for Spatially Distributed Controllers with Sparsity Constraints
论文作者
论文摘要
在本文中，我们研究了分布式系统的线性时间存在状态反馈控制器设计问题。我们遵循最近开发的系统水平合成（SLS）方法，并在所得的闭环映射上施加了局部性结构。相应的控制器实现继承了此规定的结构。与现有的SLS结果相反，我们得出了所有可实现的稳定闭环的明确（而不是隐式）参数化。这接受了闭环动力学的时间部分的更有效的IIR表示，并且允许将H2设计问题带有闭环空间稀疏约束，将其转换为标准模型匹配问题，并具有传输函数参数的数量，其数量通过封闭式空间范围约束线性地缩放。我们通过两种应用来说明结果：一阶子系统的共识和车辆排量问题。在一阶共识的情况下，我们提供分析解决方案并进一步分析所得控制器实现的体系结构。提出了无限范围内空间不变系统的结果，以洞悉大量但有限的子系统的情况。
In this article, we study the linear time-invariant state-feedback controller design problem for distributed systems. We follow the recently developed system level synthesis (SLS) approach and impose locality structure on the resulting closed-loop mappings; the corresponding controller implementation inherits this prescribed structure. In contrast to existing SLS results, we derive an explicit (rather than implicit) parameterization of all achievable stabilized closed-loops. This admits more efficient IIR representations of the temporal part of the closed-loop dynamics, and it allows for the H2 design problem with closed-loop spatial sparsity constraints to be converted to a standard model matching problem, with the number of transfer function parameters scaling linearly with the closed-loop spatial extent constraint. We illustrate our results with two applications: consensus of first-order subsystems and the vehicular platoons problem. In the case of first-order consensus, we provide analytic solutions and further analyze the architecture of the resulting controller implementation. Results for infinite extent spatially invariant systems are presented to provide insight to the case of a large but finite number of subsystems.
