(644d) Graph Convolutional Network (GCN)-Based Adaptive Distributed Model Predictive Control

Model predictive control (MPC) is a powerful optimization-based control strategy for enabling safe and economic operation of industrial chemical processes [1]. Although a widespread approach to process control, centralized MPC architectures considering the optimal control problem in its monolithic formulation may be too computationally expensive to solve within the sampling time of a process system, inhibiting its application in real-time process control. To alleviate this, distributed MPC (DMPC) has become a popular approach whereby the centralized control problem is decomposed into constituent subsystem controllers which can be solved in parallel and coordinated to reach a consensus solution to the original problem [2, 3]. DMPC reduces the computational cost of solving the control problem without significantly sacrificing control performance. In our previous work, we identified that the choice of leveraging a centralized or distributed control strategy under fixed computational budgets depends on the time-varying parameters of the control problem and that implementing a portfolio of solution strategies improves the overall control performance. It was found that the time-varying parameters of the problem, such as set points, state measurements, and disturbance values, influence the computational cost of solving the control problem such that it is preferable to use DMPC far from the desired set point when the computational cost is high and to centralize control when variables are near the operational set point and computational costs are low.

Designing an appropriate DMPC architecture is a non-trivial task and typically relies on network theoretic tools to design constituent subsystems that preserve strongly linked dynamics with minimum coordination costs [4, 5]. The DMPC architecture employed in our previous studies was based on modularity maximization of the graph representation for a process system. Through extensive simulations across various set point tracking problems, we have observed that the parameters of the problem also influence not only the computational effort for solving the centralized control problem, but also the coordination costs for DMPC, which is not accounted for in existing network-based methods for generating DMPC architectures. Moreover, recent work has also shown that adaptive DMPC architectures may improve the overall control performance compared to architectures derived solely from structural couplings [6]. Motivated by this, we develop a graph-classifier based approach for selecting the optimal DMPC architecture based simultaneously on the structural coupling of variables and their measurements and set points. The control problem of a modified cascading CSTR system [7] is presented as a variable graph where nodes represent variables in the system and edges represent constraint connectivity. Various DMPC architectures based on intuition, input-output sensitivities, and modularity maximization are derived. Training data for our Graph Convolutional Network (GCN)-based classifier is generated by simulating the various DMPC architectures across a range of control problems. In online testing, disturbance and set point information is embedded into the nodes and the previously learned neutral network weights associated with message passing and pooling are used to propagate the parameter information into the structure, generating a new graph that is classified into an optimal DMPC architecture [8]. We show that the graph-classifier identifies decompositions that lump large parameter variations, mitigating the communication costs between distributed agents. By implementing the graph-classifier into the process control loop, improved closed-loop control under fixed computational budgets is achieved by the adaptive DMPC approach compared to a decomposition based strictly on structural coupling of variables.

References:

[1] James B. Rawlings, David Q. Mayne, and Moritz M. Diehl. Model Predictive Control: Theory, Computation, and Design. Nob Hill Publishing, LLC, 2022

[2] Liu, J., Munoz de la Pena, D., Christofides, P. D. Distributed model predictive control of nonlinear process systems. AIChE J. (55), 2009, pp. 1171-1184

[3] Stewart, B.T., Wright, S.J., Rawlings, J.B. Cooperative distributed model predictive control for nonlinear systems. J. Proc. Con. (21), 2011, pp. 698-704

[4] Tang, W., Allman, A., Daoutidis, P. Optimal decomposition for distributed optimization in nonlinear model predictive control through community detection. Comp. Chem. Eng. (111), 2018, pp. 43–54

[5] Pourkargar, D., Manjiri, M., Almansoori, A., Daoutidis, P., Distributed estimation and nonlinear model predictive control using community detection. Ind. & Eng. Chem. Res., (58), 2019, pp 13495–13507.

[6] Ebrahimi, A, Pourkargar, D. Multi-agent distributed control of integrated process networks using an adaptive community detection approach. Digital Chem. Eng. (11), 2024

[7] Yin, X., Qin, Y., Liu, J., Huang, B. Data-driven moving horizon state estimation of nonlinear processes using Koopman operator. Chem. Eng. Res. & Des. (200), 2024, pp 481-492

[8] Kipf, T., Welling, M. Semi-Supervised Classification with Graph Convolutional Networks, arXiv:1609.02907