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Robust model predictive control for large-scale distributed parameter systems under uncertainty

Min Tao, Ioannis Zacharopoulos, Constantinos Theodoropoulos

Abstract

Control of nonlinear distributed parameter systems (DPS) under uncertainty is a meaningful task for many industrial processes. However, both intrinsic uncertainty and high dimensionality of DPS require intensive computations, while non-convexity of nonlinear systems can inhibit the computation of global optima during the control procedure. In this work, polynomial chaos expansion (PCE) was used to account for the uncertainties in quantities of interest through a systematic data collection from the high-fidelity simulator. Then the proper orthogonal decomposition (POD) method was adopted to project the high-dimensional nonlinear dynamics of the computed statistical moments/bounds onto a low-dimensional subspace, where recurrent neural networks (RNNs) were subsequently built to capture the reduced dynamics. Finally, the reduced RNNs based model predictive control (MPC) would generate a set of sequential optimisation problems, of which near global optima could be computed through the mixed integer linear programming (MILP) reformulation techniques and advanced MILP solver. The effectiveness of the proposed framework is demonstrated through two case studies: a chemical tubular reactor and a cell-immobilisation packed-bed bioreactor for the bioproduction of succinic acid.

Robust model predictive control for large-scale distributed parameter systems under uncertainty

Abstract

Control of nonlinear distributed parameter systems (DPS) under uncertainty is a meaningful task for many industrial processes. However, both intrinsic uncertainty and high dimensionality of DPS require intensive computations, while non-convexity of nonlinear systems can inhibit the computation of global optima during the control procedure. In this work, polynomial chaos expansion (PCE) was used to account for the uncertainties in quantities of interest through a systematic data collection from the high-fidelity simulator. Then the proper orthogonal decomposition (POD) method was adopted to project the high-dimensional nonlinear dynamics of the computed statistical moments/bounds onto a low-dimensional subspace, where recurrent neural networks (RNNs) were subsequently built to capture the reduced dynamics. Finally, the reduced RNNs based model predictive control (MPC) would generate a set of sequential optimisation problems, of which near global optima could be computed through the mixed integer linear programming (MILP) reformulation techniques and advanced MILP solver. The effectiveness of the proposed framework is demonstrated through two case studies: a chemical tubular reactor and a cell-immobilisation packed-bed bioreactor for the bioproduction of succinic acid.

Paper Structure

This paper contains 11 sections, 30 equations, 20 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. PCE-POD-RNN based robust NMPC Methodology
  3. Problem formulation
  4. Polynomial chaos expansion
  5. Proper orthogonal decomposition
  6. Recurrent neural network
  7. Nonlinear model predictive control
  8. Case studies
  9. Chemical tubular reactor
  10. Packed-bed bioreactor with immobilised cells
  11. Conclusion

Figures (20)

  • Figure 1: From fold RNN to unfold RNN
  • Figure 2: Block diagram of reduced models based observer and NMPC structure
  • Figure 3: An exothermic tubular reactor with reaction A$\rightarrow$ B
  • Figure 4: Comparison of full order and POD-RNN time profiles of $\mathbb{E}(C(y1,t))$ and $T^{up}(y1,t)$ at the exit of the tubular reactor
  • Figure 5: Comparison of full order and POD-RNN space profiles of $\mathbb{E}(C(y1,t))$ and $T^{up}(y1,t)$ at steady state
  • ...and 15 more figures