Networked model predictive control of spatially distributed processes

Abstract

This work focuses on networked model predictive control (MPC) of spatially distributed processes modeled by parabolic partial differential equations (PDEs) with sensor measurements that are transmitted to the controller over a resource-constrained communication medium. The objective of our work is to enforce the desired stability properties with minimal sensor-controller information exchange. To this end, a Lyapunov-based MPC is designed on the basis of a Lyapunov-based analytical bounded controller which is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. Unlike conventional Lyapunov-based MPC formulations, the sensors do not have to transmit the measurements at a fixed rate; instead an adaptive communication strategy is applied to switch on or off the communication over the network. The key idea is to monitor the model estimation error at each sampling time and suspend communication for periods when the prescribed stability conditions obtained based on the forecasted evolution of the Lyapunov function are satisfied. When the model estimation error grows and fails to satisfy the stability conditions, which indicates the possible loss of stability in the future, the sensors are prompted to send their measurements and the model estimation error is reset to zero in order to ensure closed-loop stability. Finally, the implementation of the results is illustrated using a representative diffusion-reaction process example.