Feedback Control Over Noisy Channels: Characterization of a General Equilibrium

In this article, we study an energy-regulation tradeoff that delineates the fundamental performance bound of a feedback control system over a noisy channel in an unreliable communication regime. The channel and the process are modeled by an additive white Gaussian noise channel with fading and a partially observable Gauss-Markov process, respectively. Moreover, the feedback control loop is constructed by designing an encoder with a scheduler and a decoder with a controller. The scheduler and the controller are the decision makers deciding about the transmit power and the control input at each time, respectively. Associated with the energy-regulation tradeoff, we characterize an equilibrium at which neither the scheduler nor the controller has a unilateral incentive to deviate from its policy. We argue that this equilibrium is a general one as it attains global optimality without any restrictions on the information structure or the policy structure, despite the presence of signaling and dual effects.