(309d) Optimization-Based Event-Triggered Predictive Control of Process Systems with Control and Communication Constraints

The design and analysis of networked control systems have been the subject of significant research interest over the last two decades, both in the industrial and academic circles (e.g., see [1]-[3] for surveys of results in this area). The operational flexibility and substantial economic savings realized through networked control architectures have been a major driving force behind the increased reliance in industrial practice on sensor and control systems that are accessed over shared communication networks. The integration of wireless sensor networks in process control systems, for example, is an appealing goal that promises to expand the capabilities of existing control technology beyond what is possible with wired devices alone, and is regarded as a key enabling mechanism for the transition towards smart plant operations [4]. At the same time, the various fundamental challenges introduced by this technology from a control point of view have motivated numerous research studies. One of the key challenges is the development of resource-aware control methods that can systematically balance the desired stability and performance requirements against the intrinsic constraints on the sensing, computation and communication resources of the networked devices as well as the occasional unreliability of the communication medium due to interference in the field or environmental impact. On the one hand, maximizing control system performance often requires frequent sensor-controller communication and increased levels of network resource utilization. Reducing communication costs, on the other hand, favors keeping the sensing and communication levels to a minimum which can lead to reduced control system performance.

A common approach for dealing with communication constraints in networked control systems is the use of event-triggered control strategies. In these strategies, sensor-controller communication over the network is typically suspended or restored in response to certain events which are tied to some specified closed-loop stability and/or performance thresholds. The aim is to keep network utilization to a minimum while guaranteeing minimal levels of control performance. The approach typically starts with the design of a model-based stabilizing feedback controller and ends with the derivation of a constant or state-dependent stability threshold which is used as a trigger for sensor-controller communication. The implementation generally involves monitoring the model estimation error during periods of communication suspension and updating the model states in the event that the stability threshold is breached. This approach is appealing in the context of sensor/actuator networks where reducing network utilization can also reduce the energy expenditures of battery powered wireless devices, and has been widely studied in recent years (e.g., see [5]â??[8] for some results in this area).

The appealing features of this approach notwithstanding, a close examination of existing event-triggered control strategies reveals a general lack of explicit control performance optimization and constraint handling capabilities in the controller design methodology. In the context of balancing the intrinsic tradeoff between control performance and network resource utilization, there is an apparent increased emphasis on reducing network utilization, often at the expense of control system performance. In addition to the lack of performance optimization considerations, practical implementation considerations such as the presence of constraints on the state and manipulated variables, which are commonly encountered in practical applications, are also ignored in the design formulation. These considerations not only limit the achievable control quality but can also lead to closed-loop instability if not explicitly accounted for at the controller design stage.

Motivated by these considerations, we present in this work an optimization-based event-triggered control methodology for systems subject to state, control and sensor-controller communication constraints. The objective is to optimize the control system performance while minimizing communication costs and network utilization at the same time. To this end, a model-based state-feedback controller is initially designed and used to obtain a state-dependent stability threshold which is used as the basis for event-triggered communication. An explicit characterization of the threshold -- in terms of the model and controller design parameters -- is obtained via Lyapunov techniques and used to provide an explicit link between the communication cost and the choice of controller design parameters. A finite-horizon optimal control problem in which the objective function includes explicit penalties on the states, the control action and the extent of sensor-controller communication is then formulated subject to the appropriate state, control and stability constraints. The penalty placed on the sensor-controller communication in the objective function is derived directly from the communication-triggering threshold. The optimization problem is solved in a receding horizon fashion to obtain the optimal controller design parameters over the horizon. Unlike conventional model predictive control formulations, however, the optimization problem is re-solved and the model states are updated only at times when the communication threshold is breached. To this end, the model estimation error is monitored at each sampling time, and communication is restored when the stability threshold is violated. In addition to reducing sensor-controller communication costs and optimizing system performance, the resulting reduction in the computational load associated with the proposed on-line optimization scheme is another appealing feature, especially in the context of nonlinear systems. Finally, the developed methodology is tested and illustrated using a simulated chemical process example.

References:

[1] J. P. Hespanha, P. Naghshtabrizi, and Y. Xu, â??A survey of recent results in networked control systems,â? Proc. of IEEE, vol. 95, pp. 138â??162, 2007.

[2] R. A. Gupta, â??Networked control systems: Overview and and research trends,â? IEEE Trans. Ind. Electron., vol. 57, pp. 2527â??2535, 2010.

[3] K.-Y. You and L.-H. Xie, â??Survey of recent progress in networked control systems,â? Acta Automatica Sinica, vol. 39, pp. 101â??117, 2013.

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

[5] 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.

[6] 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.

[7] 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.

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