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.

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