An Explicit Parametrization of Closed Loops for Spatially Distributed Controllers With Sparsity Constraints
An Explicit Parametrization of Closed Loops for Spatially Distributed Controllers With Sparsity Constraints
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DOI：
10.1109/tac.2021.3111863
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发表时间：
2020-12
影响因子：
6.8
通讯作者：
E. Jensen;Bassam Bamieh
中科院分区：
文献类型：
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作者：
E. Jensen;Bassam Bamieh
在本文中，我们研究分布式系统的线性时不变状态反馈控制器设计问题。我们遵循最近开发的系统级综合（SLS）方法，并将局部结构强加于所得的闭环映射上；相应的控制器实现继承了这个规定的结构。与现有的 SLS 结果相比，我们得出了所有可实现的稳定闭环的显式（而不是隐式）参数化。这允许对闭环动力学的时间部分进行更有效的 IIR 表示，并且允许将具有闭环空间稀疏约束的 $\mathcal {H}_2$ 设计问题转换为标准模型匹配问题，其中传递函数参数的数量随闭环空间范围约束线性缩放。我们用两个应用来说明我们的结果：一阶子系统的共识和车辆排问题。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最终控制器实现的架构。给出了无限范围空间不变系统的结果，以深入了解大量但有限数量的子系统的情况。
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 $\mathcal {H}_2$ 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.