(412d) Networked Model Predictive Control of Spatially Distributed Processes

Control over communication networks has attracted considerable attention in recent years in both the academic and industrial research communities. The use of wireless networks in process control systems, for example, allows for modular and flexible system design (e.g. distributed processing and inter-operability), simple and fast implementation, and reduced installation and maintenance costs. However, the integration of communication networks in general (and wireless networks in particular) introduces a number of challenges due to the intrinsic limitations on the collection, processing and transmission capabilities of the measurement system and the communication medium. These challenges have been a major driving force behind an extensive and growing body of research work on networked control of dynamic systems, particularly those modeled by lumped parameter systems. In recent years, a number of efforts have also been made towards the development of a methodology for networked control of spatially-distributed systems modeled by partial differential equations (PDEs) that arise naturally in the modeling of transport-reaction processes and fluid flows [1],[2]. The focus of these efforts has been primarily on achieving closed-loop stability with minimal network resource utilization. This is an appealing objective given that it reduces the susceptibility of the networked control system to communication disruptions. Beyond the stabilization objective, performance and optimality requirements, as well as the handling of constraints on the process states and inputs, are key objectives that need to be addressed in the design of any process control system. One of the few systematic methods suited for incorporating performance objectives and constraint handling is Model Predictive Control (MPC), which is based on iterative, finite-horizon optimization of a plant model. At this stage, systematic methods for networked predictive control of spatially distributed systems remain lacking and in need of development.

In this contribution, we develop and present a framework for networked model predictive control of spatially distributed processes modeled by parabolic PDEs with sensor measurements that are transmitted to the controller over a resource-constrained communication medium. The aim of this work is to enforce the desired stability and optimality properties with minimal sensor-controller information exchange. To this end, a finite-dimensional approximate model is initially obtained using model reduction techniques to capture the dominant dynamics of the infinite-dimensional system, and is then used to design a Lyapunov-based model predictive controller (LMPC) that enforces closed-loop stability for a given sensor-controller communication rate. The control action is generated by solving a model-based finite-horizon optimization problem based on an appropriate cost functional subject to constraints on the process dynamics, states and inputs. The controller guarantees the decay of the Lyapunov function over each sampling interval within a well-defined stability region. Unlike conventional LMPC formulations, however, the sensors do not transmit the measurements at a fixed rate, but instead communicate with the controller in an adaptive fashion. The key idea is to monitor the evolution of the Lyapunov function at the sampling times and suspend communication for periods when the prescribed stability threshold is satisfied. During such periods, the predictive controller relies on the available model to estimate the slow states of the infinite-dimensional system, and computes the control action using an open-loop optimization formulation. At times when the sampled state begins to breach the expected stability threshold, communication is restored and the controller switches back to using the sampled measurements to update the model predictions and repeat the optimization at each sampling time. Finally, the implementation of the finite-dimensional networked control structure on the infinite-dimensional system is analyzed, and the results are illustrated using a representative diffusion-reaction process example.

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.

[2] Yao, Z. and N. H. El-Farra, ``Resource-Aware Scheduled Control of Distributed Process Systems Over Wireless Sensor Networks," Proceedings of American Control Conference, pp. 4121-4126, Baltimore, MD, 2010.