(386f) Dynamic Reconfiguration for Modular Facilities Using Machine Learning Assisted Mixed-Integer Nonlinear Model Predictive Control

Mixed-integer model predictive control (MPC) allows for discrete variables to be optimized with continuous-valued control decisions in a feedback control law. The presence of discrete decisions, which are a common feature in industrial processes, renders the optimization problem more significantly difficult to solve than a traditional continuous problem. Mixed-integer linear/quadratic problems can usually be efficiently solved by multiple iterations of continuous relaxations of integer constraints using a branch and bound approach[1]. However, despite the impressive advances made in solving nonconvex mixed-integer nonlinear programs to global optimality[2], it is still extremely challenging to deploy this approach online and achieve solutions in a relevant amount of time. Even if some approximations for MINLP are used, such as piecewise affine approximations[3], or combinatorial integral approximation[4], the trade-off between computing cost and controller performance becomes nonnegligible for large-scale industrial processes.

In this work, we present an approach to determine integer control decisions a priori to solving the MPC problem using data-driven machine learning algorithms. Our previous work[5] considered control of numbered-up modular systems with fixed configurations, and which demonstrated that operational conditions could affect selection of the optimal configuration of modules. Data are obtained by solving the optimal control problem at various set points or initial conditions, and identifying the corresponding optimal configuration which has the smallest performance index on the final output concentration. After learning these data by machine learning approaches including support vector machines (SVM), decision trees, and k-nearest neighbors (KNN), we obtain several mathematical guidelines for reconfiguration to help the online MPC quickly make decisions on dynamically selecting the optimal configuration. Principal component analysis is implemented to identify the parameters that have the largest effect on the configuration decision making. Since reconfiguration decisions can be considered as integer variables in the MPC problem, we also build an MINLP MPC to dynamically switch configurations for the similar control problem with affine approximations and combinatorial integral approximations respectively as comparison.

To demonstrate the efficacy of the proposed approach, we present the control performance of a benchmark system with three modular nonisothermal CSTR's operating in four potential configurations[5]. Results demonstrate that SVM classifier has the greatest accuracy on predicting the optimal configurations than other two methods. All classifiers suggest that disturbances on the feeding stream temperature, setpoint of the final output concentration, and initial concentration of each individual modular unit are the principle components that most strongly impact the classifier on selecting optimal configurations. Compared to the MPC with fixed configurations[5], the MPC with machine learning classifiers for reconfiguration gives better control performance of shorter recovering time and smaller deviation from the setpoint. Moreover, this proposed reconfigurable MPC performs much faster than solving the MINLP directly for MPC, with minimal degradation in control performance.

[1] R. D. McAllister and J. B. Rawlings, “Advances in mixed-integer model predictive control,” in 2022 American Control Conference (ACC). IEEE, 2022, pp. 364–369.

[2] M. R. Kılın ̧c and N. V. Sahinidis, “Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with baron,” Optimization Methods and Software, vol. 33, no. 3, pp. 540–562, 2018.

[3] J. B. Rawlings, N. R. Patel, M. J. Risbeck, C. T. Maravelias, M. J. Wenzel, and R. D. Turney, “Economic mpc and real-time decision making with application to large-scale hvac energy systems,” Computers & Chemical Engineering, vol. 114, pp. 89–98, 2018.

[4] A. B ̈urger, C. Zeile, A. Altmann-Dieses, S. Sager, and M. Diehl, “Design, implementation and simulation of an mpc algorithm for switched nonlinear systems under combinatorial constraints,” Journal of Process Control, vol. 81, pp. 15–30, 2019.

[5] Y. Dai, S. Fay, and A. Allman, “Analysis of model predictive control in numbered-up modular facilities,” Digital Chemical Engineering, vol. 7, p. 100088, 2023