The Role of Communication Delays in the Optimal Control of Spatially Invariant Systems

• 成果类型: Article
• 署名作者: Ballotta, Luca; Arbelaiz, Juncal; Gupta, Vijay; Schenato, Luca; Jovanovic, Mihailo R.
• 署名单位: Delft University of Technology; Princeton University; Purdue University System; Purdue University; University of Padua; University of Southern California
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3601758
• 发表日期: 2026
• 关键词: Distributed control; consensus; DESIGN

摘要

We study optimal proportional feedback controllers for spatially invariant systems when the controller has access to delayed state measurements received from different spatial locations. We analyze how delays affect the spatial locality of the optimal feedback gain leveraging the problem decoupling in the spatial frequency domain. For the cases of expensive control and small delay, we provide exact expressions of the optimal controllers in the limit for infinite control weight and vanishing delay, respectively. In the expensive control regime, the optimal feedback control law decomposes into a delay-aware filtering of the delayed state and the optimal controller in the delay-free setting. Under small delays, the optimal controller is a perturbation of the delay-free one, which depends linearly on the delay. We illustrate our analytical findings with a reaction-diffusion process over the real line and a multiagent system coupled through circulant matrices, showing that delays reduce the effectiveness of optimal feedback control and may require each subsystem within a distributed implementation to communicate with farther-away locations.