Robust stabilization of sampled-data distributed processes using a dynamic sensor-controller communication logic

This paper presents a methodology for the robust stabilization of spatially distributed processes with sampled sensor measurements that are transmitted to the actuators over a resource-constrained communication medium. Initially, a finite-dimensional system that captures the slow process dynamics is derived and used to design a Lyapunov-based controller that enforces closed-loop stability in the absence of communication suspensions. An explicit characterization of the stability properties of the closed-loop system under discrete measurement sampling is obtained and then used to devise a dynamic communication logic which can adaptively adjust the rate of information transfer from the sensors to the controller. The key idea is to monitor the evolution of the Lyapunov function at the sampling times and suspend communication for periods when the prescribed stability threshold is satisfied. During such periods, the controller switches to a finite-dimensional model that provides estimates of the slow states to compute the control action. At times when the sampled state begins to breach the expected stability threshold, communication is restored and the controller switches back to the sampled measurements. The results are illustrated through an application to a representative diffusion-reaction process.