Model-Based Networked Control of Spatially Distributed Systems with Measurement Delays

This work focuses on model-based control of spatially distributed processes, modeled by highly dissipative nonlinear partial differential equations (PDEs), using delayed measurements that are transmitted to the controller over a resource-constrained communication network. The control objective is to enforce closed-loop stability with minimal sensor-controller communication while simultaneously accounting for the delayed arrival of the measurements. To address the problem, a model-based controller is initially designed on the basis of an approximate finite-dimensional model that captures the slow dynamics of the infinite-dimensional system. The model provides the controller with estimates of the slow states at times when sensor-controller communication is suspended, and the model state is updated when state measurements become available. To compensate for the effect of the delay, the controller includes a finite-dimensional propagation model that uses the delayed measurement, together with the past values of the control input, to provide an estimate of the current slow state which is then used to update the state of the model. By formulating the networked closed-loop system as a switched system and analyzing the evolution of the model estimation and propagation errors, a sufficient condition for closed-loop stability and ultimate boundedness of the finite-dimensional networked closed-loop state is obtained. Finally, the results are illustrated using a diffusion-reaction process example.