(515a) Networked Control of Spatially Distributed Systems: Handling Communication Constraints and Delays

The focus of this contribution is on the design of networked control systems for spatially distributed processes modeled by highly-dissipative partial differential equations (PDEs) with sensor-controller communication constraints and delays. This is an important problem given the increased reliance of process operation on networked sensors and controls, and the abundance of process systems characterized by spatial variations, such as transport-reaction processes and fluid flow systems. A key consideration in the design of the networked control system is the ability to enforce closed-loop stability with minimal sensor-controller information transfer to aggressively conserve limited network resources. In addition to resource constraints, sensor-controller communication delays represent an important issue that requires attention in the networked control system design to avoid potential instability or performance deterioration. To address these problems, we include within the networked control system: (1) an approximate finite-dimensional model that provides the controller with an estimate of the slow state of the infinite-dimensional system when communication is suspended to reduce information transfer, and (2) a propagation unit that compensates for the communication delay by using the model, together with the past control inputs, to calculate an estimate of the current output from the received delayed measurements. The model state is then updated using the latter estimate at discrete time instances. The networked closed-loop system is analyzed using a combination of tools from switched systems, infinite-dimensional systems and singular perturbations, leading to precise characterizations of the interplays between the minimum allowable sensor-controller communication rate, the finite-dimensional model order and accuracy, the delay size, and the selection of actuator and sensor configurations. Finally, the theoretical results are illustrated using a transport-reaction process example.