(582f) Sampled-Data Event-Triggered Control of Distributed Parameter Systems with Networked Sensors and Actuators

With the emergence of the Smart Plant paradigm in recent years [1] and the shift in industrial practice towards sensor and control systems that are accessed over shared communication networks instead of dedicated links, a significant and growing body of research work aimed at addressing the fundamental challenges associated with the design and analysis of networked control systems has emerged. A close examination of the literature on this topic, however, shows that the bulk of existing studies have focused on spatially homogenous systems whose underlying dynamics are modeled by systems of ordinary differential or difference equations. In contrast, spatially distributed systems whose underlying dynamics are captured by systems of Partial Differential Equations (PDEs) have received less attention. This is an important limitation given the fact that many industrial processes are characterized by spatial variations (e.g., transport-reactions and fluid flows), and that the control of these systems typically involves the use of spatially distributed control actuators and measurement sensors.

A number of recent studies have been carried out to bridge this gap (e.g., see [2]â??[3] for some efforts in this direction). Bringing together tools from infinite-dimensional systems, model reduction and model-based control, the focus of these studies has been primarily on the development of systematic networked control methodologies that address various sensor-controller communication constraints, such as network resource limitations, communication delays, and real-time scheduling constraints. The problem is generally addressed by embedding a reduced-order model of the infinite-dimensional system in the control system. The model is used to generate the necessary control action when sensor-controller communication is suspended and is updated when communication is permitted using a time-triggered sensor-controller communication policy with a constant update rate.

An alternative approach for dealing with communication constraints in networked control systems is the use of event-triggered control strategies, where communication over the network is suspended or restored in response to certain events which are tied to the breach of certain desired closed-loop stability and/or performance thresholds. The aim is to keep network utilization to a minimum while guaranteeing desired levels of control performance. This is an appealing goal in the context of sensor/actuator networks where reducing network utilization can also reduce the energy expenditures of battery powered wireless devices. This approach has been widely studied in the context of lumped parameter systems (e.g., see [4]â??[6]), and has also received some attention in the distributed parameter system setting [7]-[8]. In these studies, however, practical implementation issues such as the discrete availability of sampled state measurements, were not considered, and no assessment of the stability or performance properties of the networked closed-loop system under discretely-sampled measurements was made. In practice, state measurements are often sampled at discrete times. The limited access to state measurements during sampling intervals poses an important obstacle for the implementation of event-triggered control systems as it restricts the system's ability to properly monitor and evaluate the communication-triggering events, which typically involve state-dependent thresholds. A common approach for dealing with sampled-data control systems is the use of zero-order-hold schemes, which hold the last available measurement static until the next sampled measurement arrives. However, this approach does not take the system dynamics into account and can therefore lead to closed-loop instability when used to implement the event-triggered communication strategy.

Motivated by these considerations, we present in this work an event-triggered control strategy for spatially distributed systems with low-order uncertain dynamics, sensor-controller communication constraints and discretely-sampled state measurements. Based on a suitable finite-dimensional model that approximates the dominant dynamics of the infinite-dimensional system, an event-triggered networked control system that enforces closed-loop stability with minimal sensor-controller communication is initially designed for the case when state measurements are sampled continuously. The model is used by the controller to generate the necessary control action when communication is suspended, and its state is updated using the real-time measurements when communication is restored. Communication is triggered when a state-dependent threshold on the model estimation error is breached. The communication threshold is designed using Lyapunov techniques and is explicitly characterized in terms of the model and controller design parameters, as well as the actuator and sensor locations. To address the implementation of the control strategy under discretely-sampled measurements, a forecasting scheme that provides a worst-case bound on the evolution of the model estimation error over each sampling interval is devised and incorporated into the control system. This bound is used to obtain a modified (tighter) communication threshold which ensures that the actual stability threshold is not breached during periods of measurement unavailability. It is shown that if the underlying dynamics of the system are linear, the forecasting scheme can be carried out off-line leading to an explicit characterization of the modified stability threshold. On the other hand, for systems with nonlinear dynamics, an on-line forecasting strategy is required. Finally, the developed methodology is illustrated using a diffusion-reaction process example.

References:

[1] P. D. Christofides, J. F. Davis, N. H. El-Farra, D. Clark, K. R. Harris, and J. N. Gipson, â??Smart plant operations: Vision, progress and challenges,â? AIChE Journal, vol. 53, no. 11, pp. 2734â??2741, 2007.

[2] Z. Yao and N. H. El-Farra, â??Resource-aware scheduled control of distributed process systems over wireless sensor networks,â? Proceedings of American Control Conference, pp. 4121â??4126, 2010.

[3] Z. Yao and N. H. El-Farra, â??Model-based networked control of spatially distributed systems with measurement delays,â? Proceedings of American Control Conference, pp. 2990â??2995, 2012.

[4] M. Mazo and P. Tabuada, â??Decentralized event-triggered control over wireless sensor/actuator networks,â? IEEE Transactions on Automatic Control, vol. 56, no. 10, pp. 2456â??2461, 2011.

[5] X. Wang and M. D. Lemmon, â??Event-triggering in distributed networked control systems,â? IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 586â??601, 2011.

[6] E. Garcia and P. J. Antsaklis, â??Model-based event-triggered control for systems with quantization and time-varying network delays,â? IEEE Transactions on Automatic Control, vol. 58, no. 2, pp. 422â??434, 2013.

[7] Z. Yao and N. H. El-Farra, â??Resource-aware model predictive control of spatially distributed processes using event-triggered communication,â?Â Proceedings of 52th IEEE Conference on Decision and Control, pp. 3726â??3731, 2013.

[8] D. Xue and N. H. El-Farra, â??Networked event-triggered control of spatially distributed processes using a dual-mode communication strategy,â? Proceedings of 54th IEEE Conference on Decision and Control, pp. 1899â??1904, 2015.