Work

Data-Driven Koopman Operator-Based Model Predictive Control with Adaptive Dictionary Learning for Nonlinear Industrial Process Optimization

Year: 2026

Type: article

Abstract: Nonlinear model predictive control (NMPC) delivers high tracking accuracy for industrial processes but requires solving a nonlinear program at each sampling instant, limiting its applicability under tight real-time constraints. The Koopman operator provides a principled route to circumvent this limitation by embedding nonlinear dynamics into a higher-dimensional space where the evolution becomes linear, thereby reducing the online optimization to a convex quadratic program. This paper presents a Koopman-based MPC framework (K-MPC) that incorporates three algorithmic contributions. First, an adaptive radial basis function dictionary learning procedure selects lifting functions from process data, eliminating manual basis selection and improving approximation fidelity for systems with localized nonlinearities. Second, a recursive least-squares update rule adjusts the Koopman matrix online as new measurements arrive, enabling the controller to track slow parameter drifts without full model recomputation. Third, a tube-based constraint tightening strategy accounts for the residual linearization error, preserving recursive feasibility under bounded Koopman approximation mismatch. Simulations on a Van der Pol oscillator, a continuous stirred-tank reactor (CSTR), and a four-state Tennessee Eastman-inspired distillation column demonstrate that K-MPC achieves root-mean-square tracking errors within 11–16% of NMPC while reducing average per-step computation time by a factor of 14 to 18. The recursive update mechanism reduces prediction error by 80% compared to the fixed offline Koopman model when reactor feed concentration drifts by 15% from its nominal value. Ablation experiments confirm that adaptive dictionary learning and online updating each contribute measurably to closed-loop performance.

Source: Mathematics

DOI: 10.3390/math14081320

Authors: Zhihao Zeng, Hao Wang, Yahui Shan

Institutions: Guangdong University of Technology, Wuhan Ship Development & Design Institute

Language: English

Topic: Advanced Control Systems Optimization

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Natural Science Foundation of Hubei Province