Abstract
We examine the problem of designing the encoding and control policies of a linear stochastic control system, where the communication channel between the plant state observer (sensor) and the controller is a lossy wireless channel that is constrained in terms of transmit power and bandwidth. For a first-order ARMA modeled plant with Gaussian statistics, when there are two sensors observing the plant, nonlinear encoding is shown to result in smaller cost at time instant [Formula: see text] compared to the linear schemes, if transmissions are carried out over parallel Gaussian independent channels. In this paper, optimal linear coding schemes for the case of multiple sensors are examined. They are shown to minimize the control cost at the infinite time horizon, when the wireless channel is accessed using time division multiplexing. Our analysis is carried out for when separation between the state estimation and control is possible, and the optimal steady state control law is certainty equivalent. The distortion lower bound for estimating the plant state is derived, along with the necessary conditions on the transmit power that minimize the steady state control cost. We also propose a linear scheme that reaches the distortion bound asymptotically under relaxed conditions.
Highlights
Wireless sensors and communication have become an integral part of closed-loop control systems in the recent years
To achieve Δl(t, M) using the linear scheme described in Lemma 2, it is required that (1) the signalling rate of the wireless channel is M times higher than the sampling rate of s(t), and (2) full cooperation is possible between the sensor nodes
We studied linear coding schemes for an linear quadratic Gaussian (LQG) control with M sensors for plant observation and an AWGN communication channel between the sensors and controller of constrained bandwidth and transmit power
Summary
Wireless sensors and communication have become an integral part of closed-loop control systems in the recent years. In the case that the observation noise is additive memoryless Gaussian, optimality of linear encoding and control still holds when the noisy observations are transmitted over parallel Gaussian channels [3] If we extend this setting to one that includes two sensor nodes, we arrive at a rather different result. When both sensors are used to measure the plant state with certain observation noise, their measurements are correlated If these measurements (intercorrelated Gaussian) are transmitted over two parallel Gaussian channels, it was shown in [4] that for time horizon of T = 1, a nonlinear encoding scheme can result in a lower LQG cost, compared to the optimal linear strategy.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
