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

TL;DR

This paper presents a robust control framework for large-scale nonlinear distributed parameter systems under uncertainty, combining polynomial chaos, POD, RNNs, and MILP to efficiently compute near-global optimal control solutions.

Contribution

It introduces a novel integrated approach using PCE, POD, RNNs, and MILP for efficient robust control of high-dimensional uncertain systems.

Findings

Effective control of complex systems demonstrated in case studies.

Near-global optimal solutions achieved with MILP reformulation.

Framework reduces computational complexity for large-scale systems.

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.