(711d) Dynamic Actuator Scheduling in Networked Distributed Processes Using a Receding-Horizon Optimization Approach

One of the fundamental problems that has received significant attention in the context of control of distributed parameter systems is the optimal placement and scheduling of control actuators. The realization that the selection of the control actuator locations in a spatially-distributed control system has a significant influence not only on the controllability and stabilizability of the infinite-dimensional system but also on the achievable closed-loop performance has motivated numerous research studies on this problem. The literature on this topic is quite extensive. A few examples of works in this area include the development of a methodology for the computation of optimal locations of point control actuators for non- linear feedback controllers in transport-reaction processes described by quasi-linear parabolic PDEs [1], the use of the notions of spatial and modal controllability to formulate the optimal actuator placement for linear parabolic PDEs [2], the development of control actuator scheduling policies for fault-tolerant control [3] and constrained stabilization of parabolic PDEs [4], and the development of integrated controller and actuator switching policies aimed at improving closed-loop performance and compensation of spatiotemporally varying disturbances [5].

A close inspection of the available results, however, shows that the emphasis of existing formulations is placed on optimizing the closed-loop system performance, with respect to the response speed and the control effort, without considering the cost associated with the sensor-controller communication. This cost is an increasingly important consideration in the design of feedback control systems for processes controlled over resource-constrained communication networks. Sensor and control systems that are accessed over bandwidth-limited communication channels are commonplace in many modern industrial systems due to the appealing economic savings and operational flexibility that networked control systems provide. For these systems to fulfill their promise, however, a balance must always be maintained between the extent of network utilization, on the one hand, and the achievable closed-loop performance, on the other. Keeping communication costs to a minimum favors reduced network utilization whereas maximizing closed-loop performance requires the opposite.

While research on networked control systems has been extensive (see [6], [7] for some surveys of results in this area), results on the analysis and design of networked control systems for spatially distributed systems have been more limited by comparison. A number of efforts have been made in recent years to address this problem by leveraging tools and techniques from infinite-dimensional systems, model reduction and model-based control (e.g., see [8]–[10]). The focus of these studies has been on ensuring closed-loop stability with reduced sensor-controller communication and explicitly characterizing the closed-loop stability properties in terms of the different control and communication design parameters. While the resulting characterizations establish a direct linkage between the placement of the control actuators and the level of network utilization, the problem of how to optimally select or schedule the control actuators in a way that simultaneously optimizes the closed-loop performance and communication costs has not been considered in previous works.

Motivated by these considerations, we present in this work a methodology for the integrated dynamic scheduling of control actuators and communication in a class of networked distributed processes using an optimization-based formulation. The objective is to simultaneously optimize the control system performance and minimize sensor-controller communication costs. We focus on processes modeled by uncertain PDEs with intrinsically low-order dominant dynamics. Based on an approximate low-order model that captures the dominant dynamics of the infinite-dimensional system, a model-based state feedback controller is initially designed and its closed-loop stability properties are explicitly characterized in terms of the model update period and the feasible control actuator locations. Based on this characterization, a finite-horizon optimization problem is formulated and solved on-line to determine the control actuator locations and update rates that simultaneously optimize closed-loop performance and sensor-controller network resource utilization. To this end, an objective function that includes suitable penalties on the response speed, the control effort and the model update frequency is formulated subject to appropriate closed-loop stability constraints. The optimization problem is solved in a receding horizon fashion resulting in an integrated dynamic scheduling policy that varies the control actuator placement and communication rate and allow the process to cope with its uncertain operating environment. The developed methodology is illustrated and evaluated through an application to a simulated diffusion-reaction process example.

References:

[1] C. Antoniades and P. D. Christofides, “Computation of optimal actuator locations for nonlinear controllers in transport-reaction processes,” Comp. & Chem. Eng., vol. 24, pp. 577–583, 2000.

[2] A. Armaou and M. Demetriou, “Optimal actuator/sensor placement for linear parabolic PDEs using spatial H2 norm,” Chem. Eng. Sci., vol. 61, pp. 7351–7367, 2006.

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[7] Y. Ke-You and X. Li-Hua, “Survey of recent progress in networked control systems,” Acta Automatica Sinica, vol. 39, pp. 101–117, 2013.

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[9] Z. Yao and N. H. El-Farra, “Resource-aware model predictive control of spatially distributed processes using event-triggered communication,” in Proceedings of 52nd IEEE Conference on Decision and Control, Florence, Italy, pp. 3726–3731, 2013.

[10] D. Xue and N. H. El-Farra, “Output feedback-based event-triggered control of distributed processes with communication constraints,” in Proceedings of 55th IEEE Conference on Decision and Control, Las Vegas, NV, pp. 4296–4301, 2016.