Control Over Noisy Channels

Abstract-Communication is an important component of distributed and networked controls systems. In our companion paper we presented a framework for studying control problems with a digital noiseless communication channel connecting the sensor to the controller [TM1]. Here we generalize that framework by applying traditional information theoretic tools of source coding and channel coding to the problem. We present a general necessary condition for observability and stabilizability for a large class of communication channels. Then we study sufficiency conditions for Internet-like channels that suffer erasures

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

Rate-Cost Tradeoffs in Control

Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate r bits/sec and the expected cost b. We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. [2]. The bound applies as long as the differential entropy of the system noise is not −∞ . It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variablelength vector quantization to prove that the new converse bounds are tight

Time-triggering versus event-triggering control over communication channels

Time-triggered and event-triggered control strategies for stabilization of an unstable plant over a rate-limited communication channel subject to unknown, bounded delay are studied and compared. Event triggering carries implicit information, revealing the state of the plant. However, the delay in the communication channel causes information loss, as it makes the state information out of date. There is a critical delay value, when the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events. This occurs when the maximum delay equals the inverse of the entropy rate of the plant. In this context, extensions of our previous results for event triggering strategies are presented for vector systems and are compared with the data-rate theorem for time-triggered control, that is extended here to a setting with unknown delay.Comment: To appear in the 56th IEEE Conference on Decision and Control (CDC), Melbourne, Australia. arXiv admin note: text overlap with arXiv:1609.0959