Nonlinear distributed sensing for closed-loop control over Gaussian channels

A scenario of distributed sensing for networked control systems is considered and a new approach to distributed sensing and transmission is presented. The state process of a scalar first order linear time invariant dynamical system is sensed by a network of wireless sensors, which then instantaneously transmit their measurements to a remotely situated control unit over parallel Gaussian channels. The control unit aims to stabilize the system in mean square sense. The proposed non-linear delay-free sensing and transmission strategy is compared with the well-known amplify-and-forward strategy, using the LQG control cost as a figure of merit. It is demonstrated that the proposed nonlinear scheme outperforms the best linear scheme even when there are only two sensors in the network. The proposed sensing and transmission scheme can be implemented with a reasonable complexity and it is shown to be robust to the uncertainties in the knowledge of the sensors about the statistics of the measurement noise and the channel noise.