(250g) Choosing between Distributed and Centralized Strategies in Moving Horizon Model Predictive Control

Model predictive control (MPC) is a powerful optimization-based control paradigm for enabling safe and economic operation of chemical processes. Many MPC problems encountered in industrial process control involve large nonconvex problem spaces. The computational resources required to solve these nonconvex optimal control problems scale poorly with size and high quality solutions are often not obtainable within a computational time relevant for real-time process control. For such problems, distributed MPC has become a popular approach, whereby the optimal control problem is decomposed into smaller subproblems which are then coordinated to arrive at a solution to the original MPC problem [1,2]. Recent work [3,4] has developed community detection methods for systematically determining subproblems that are most amenable to powerful decomposition solution methods. However, while distributed methods often result in a reduction in computational time required to solve the optimal control problem, there is a tradeoff in that the solutions generated typically are not as high of quality as those obtained by solving the optimization problem monolithically (a centralized MPC strategy) [5]. Moreover, there may be instances in the moving horizon where the monolithic problem is able to be solved in a control-relevant amount of time, such that it is preferable to use centralized MPC at these time points.

This work seeks to develop classifier models that determine when to use a centralized or distributed MPC based on the parameters of the optimal control problem. A critical difference between this work and previous works learning when to decompose [6] is that in this work, the structure of the optimization problem is invariant: the underlying system model is the same at each point in the moving horizon, while only the problem parameters change. As training data, we consider solving the optimal control problem for many different set points, disturbances, and initial states using both distributed and centralized MPC. The superior solution method is the one that obtains the best objective value within the computational time budget, or, if both methods obtain the same optimal solution within the allotted budget, the method that does so faster. Based on this classification, we train different classifier models including decision trees, support vector machines, and graph neural networks based on graph representations of the dynamic process [4]. We note that the classification of which solution strategy to use is often dependent not only on the problem parameters but also on the allocated computational budget. The proposed approach is tested using a benchmark system of two reactors and a separator in series. The developed classifier model is embedded into the moving horizon MPC loop and selects at each time instance whether the distributed or centralized problem should be solved. Various disturbances and set point changes not in the original training set are tested, and the ability of the ML-enhanced approach to improve controller performance in comparison to both the centralized-only and distributed-only approaches is demonstrated.

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[2] 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

[3] Allman, A., Tang, W., Daoutidis, P. DeCODe: a community-based algorithm for generating
high-quality decompositions of optimization problems. Optim. Eng. (20), 2019, pp. 1067-1084

[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.B., Almansoori, A. Daoutidis, P. The impact of decomposition on distributed model predictive control: A process network case study. Ind. Eng. Chem. Res. (56), 2017, pp. 9606-9616.

[6] Mitrai, I., Daoutidis, P. Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decompose. arXiv preprint, 2023.