In this paper, we develop a theoretical framework for goal-oriented communication assisted by reconfigurable meta-surfaces in the context of networked control systems. The relation to goal-oriented communication stems from the fact that optimization of the phase shifts of the meta-surfaces is guided by the performance of networked control systems tasks. To that end, we consider a networked control system in which a set of sensors observe the states of a set of physical processes, and communicate this information over an unreliable wireless channel assisted by a reconfigurable intelligent surface with multiple reflecting elements to a set of controllers that correct the behaviors of the physical processes based on the received information. Our objective is to find the optimal control policy for the controllers and the optimal phase policy for the reconfigurable intelligent surface that jointly minimize a regulation cost function associated with the networked control system. We characterize these policies, and also propose an approximate solution based on a semi-definite relaxation technique.

翻译：本文针对网络控制系统中的可重构超表面辅助通信，建立了一个面向任务通信的理论框架。该框架与面向任务通信的关联在于：超表面相移的优化由网络控制任务的执行性能所引导。为此，我们考虑一个网络控制系统：一组传感器观测多个物理过程的状态，通过具有多个反射单元的可重构智能表面，经不可靠无线信道将信息传输至一组控制器；控制器基于接收信息修正物理过程的行为。我们的目标是联合求解控制器的最优控制策略与可重构智能表面的最优相位策略，以最小化网络控制系统的调控代价函数。我们给出了这些策略的解析表征，并基于半正定松弛技术提出了一种近似求解方案。