(463d) Resource-Aware Control of Spatially Distributed Processes Using An Adaptive Predictor-Corrector Strategy

The development of systematic methods for the design of networked control systems for spatially distributed systems is a fundamental problem whose practical significance encompasses a wide range of chemical and physical systems, including transport-reaction processes and fluid flows. The importance of this problem stems from the increased reliance in the process industry in recent times on sensor and control systems that are accessed over communication networks rather than dedicated links, as well as the abundance of industrial applications characterized by strong spatial variations owing to the underlying physical phenomena such as diffusion, convection, and phase-dispersion. While an extensive and growing body of research work on networked control of lumped parameter systems already exists, results for spatially-distributed systems are limited at present [1]. Major bottlenecks in this direction include the infinite-dimensional nature of distributed parameter systems, as well as the complex nonlinear and uncertain dynamics that characterize their behavior.

One of the appealing goals in the design of networked control systems -- especially those subject to resource-constraints -- is to enforce the desired closed-loop stability and performance properties with minimal sensor-controller communication. Such a resource-aware control approach is important particularly when the communication medium involves a wireless sensor network where conserving network resources is key to prolonging the service life of the network. An effort to address this problem was initiated in [1] where a methodology for the design of model-based networked control systems for spatially distributed processes described by parabolic partial differential equations (PDEs) was developed. A key idea was to reduce the transfer of information from the sensors to the controller by (1) including within the control system a finite-dimensional model that predicts the evolution of the dominant dynamic modes of the PDE and provides the controller with an estimate of those modes when measurements are not transmitted through the network, and (2) correcting the model predictions by updating the model state using the actual measurements provided by the sensors at discrete times. Under the assumption that the update period is time-invariant, an exact characterization of the minimum allowable communication rate under both full-state and output feedback control was obtained. An alternative approach is to design the networked control system in a way such that the necessary communication rate can be determined and adjusted dynamically on-line based on the state of the process. An advantage of this feedback-based communication policy is that it is more robust to unpredictable disturbances and allows the plant to respond quickly in an adaptive fashion to changes in operating conditions. Another advantage of this approach is that it ultimately leads to a more efficient utilization of network resources since the communication rate is increased only when necessary to maintain closed-loop stability.

Motivated by these considerations, we present in this work a methodology for the design of model-based resource-aware control systems for a class of spatially distributed processes modeled by nonlinear parabolic PDEs with measurement sensors that transmit their data to the controller/actuators over a resource-constrained network. Initially, model reduction techniques are used to derive an approximate finite-dimensional system that captures the dominant (slow) dynamics of the PDE. The slow subsystem is then used to design a Lyapunov-based controller that enforces closed-loop stability in the absence of communication suspensions. To reduce the frequency at which the measurements are transmitted over the network, a finite-dimensional model predictor is included within the controller to provide estimates of the slow states when measurements are not available through the network. To determine when communication must be re-established, the evolution of the Lyapunov function is monitored such that if it begins to breach a pre-specified 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 adaptively switching on and off the communication between the sensors and the controller. To address the problem when sensor measurements are only available at a finite number of locations in the spatial domain, a finite-dimensional state observer is added to generate estimates of the slow states from the available measurements and the communication logic is modified accordingly to account for the estimation errors. The implementation of the finite-dimensional networked control structure on the infinite-dimensional system is then analyzed using singular perturbation techniques. Finally, the results are illustrated through an application to a representative diffusion-reaction process.

References:

[1] Sun, Y., S. Ghantasala and N. H. El-Farra, ``Networked Control of Spatially Distributed Processes with Sensor-Controller Communication Constraints," Proceedings of American Control Conference, pp. 2489-2494, St. Louis, MO, 2009.