An Explicit Parametrization of Closed Loops for Spatially Distributed Controllers With Sparsity Constraints

• 成果类型: Article
• 署名作者: Jensen, Emily; Bamieh, Bassam
• 署名单位: University of California System; University of California Santa Barbara; University of California System; University of California Santa Barbara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3111863
• 发表日期: 2022
• 页码: 3790-3805
• 关键词: Distributed control; infinite-dimensional systems; optimal control; spatially invariant systems; system level synthesis (SLS)

摘要

In this article, we study the linear timeinvariant 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 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.