On model-based networked control of nonlinear spatially distributed systems

This work presents a framework for control of spatially distributed systems modeled by nonlinear highly-dissipative partial differential equations (PDEs) over communication networks. The framework aims to enforce closed-loop stability with minimal sensor-controller information transfer over the network. To this end, an approximate finite-dimensional model that captures the PDE's slow dynamics is used to provide the controller with estimates of the slow states when sensor-controller communication is suspended. A finite-dimensional state observer is embedded in the sensors to generate estimates of the slow states from the available measurements, and these estimates are used to update the model states whenever communication is re-established at discrete time instances. By analyzing the behavior of the overall networked closed-loop system between consecutive update times, and exploiting the stability properties of the controller and observer designs, a sufficient condition for networked closed-loop stability is obtained in terms of the sensor-controller communication rate, the model uncertainty, the controller and observer design parameters, as well as the spatial locations of the control actuators and measurement sensors. Finally, the results are illustrated through an application to the problem of stabilizing the zero solution of the Kuramoto-Sivashinsky Equation.