(16f) Robust Model Predictive Control for Large-Scale Distributed Parameter Systems Under Uncertainty

Spatiotemporal distributed parameter systems (DPS) exist widely in engineering and science. Complex DPS usually exhibit uncertainty due to inherent stochastic and/or incomplete knowledge of the process [1]. Efficient control strategy for large-scale DPS under uncertainty could speed up process production and ensure process safety [2]. However, both intrinsic uncertainty and high dimensionality would require intensive computations while non-convexity could lead to global optima issues for upper-level control [3]. Moreover, black-box characteristics of high-fidelity commercial simulators make the computational models intractable. So far, control of DPS under uncertainty is still challenging in industrial engineering.

In this work, polynomial chaos expansion (PCE) was used to account for the uncertainties in quantities of interest [4]. Then the proper orthogonal decomposition (POD) method was adopted to project the high-dimensional nonlinear dynamics onto a low-dimensional subspace through a systematic data collection from the high-fidelity simulator. The corresponding time coefficients are captured by recurrent neural networks (RNNs). Finally, model predictive control (MPC) with the reduced RNN model [5] was used to generate sequential optimization problems, which were globally solved using reformulation techniques [6]. The effectiveness of the proposed framework is demonstrated through two case studies: a chemical tubular reactor and a cell-immobilization packed-bed biochemical reactor for the bioproduction of succinic acid.

References

[1] Sullivan, T. J., 2015. Introduction to uncertainty quantification (Vol. 63). Springer.

[2] Stephanopoulos, G., & Han, C., 1996. Intelligent systems in process engineering: A review. Computers & Chemical Engineering, 20(6-7), 743-791.

[3] Theodoropoulos, C., 2011. Optimisation and linear control of large scale nonlinear systems: a review and a suite of model reduction-based techniques. In Coping with Complexity: Model Reduction and Data Analysis (pp. 37-61).Springer, Berlin, Heidelberg.

[4] Xiu, D., & Karniadakis, G. E., 2002. The Wiener--Askey polynomial chaos for stochastic differential equations. SIAM journal on scientific computing, 24(2), 619-644.

[5] Xie, W., Bonis, I., & Theodoropoulos, C., 2015. Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems. Journal of Process Control, 35, 50-58.

[6] Tao, M., & Theodoropoulos, C., 2019. Model Reduction-Based Global Optimisation for Large-Scale Steady State Nonlinear Systems. In 2019 AIChE Annual Meeting.