Networked control of spatially distributed processes using an adaptive communication policy

This work presents a model-based networked control structure with a feedback-based communication policy for spatially distributed processes modeled by highly-dissipative nonlinear PDEs with measurement sensors that transmit their data to the controller/actuators over a resource-constrained wireless sensor network. Initially, a finite-dimensional system that captures the slow dynamics of the PDE is derived and used to design a stabilizing Lyapunov-based nonlinear feedback controller. To reduce the frequency at which sensor measurements are transmitted over the network, a model of the slow subsystem is included in the control system to provide estimates of the slow states of the PDE when communication over the network is suspended. To determine when communication must be reestablished, the evolution of the Lyapunov function is monitored such that if it begins to breach a certain stability threshold at any time, the sensors are prompted to send their data over the network to update the model. Communication is then suspended for as long as the Lyapunov function continues to decay. The underlying idea is to use the Lyapunov stability constraint as the basis for switching on or off the communication between the sensors and the controller. A singular perturbation formulation is used to analyze the implementation of the networked control structure on the infinite-dimensional system. Finally, the results are illustrated through an application to a representative nonlinear diffusion-reaction process.