Adaptive Model Predictive Control for Uncertain Nonaffine Nonlinear System Based on Deep Koopman Operator
- 1School of Artificial Intelligence and Computer Science, Liaocheng University, Liaocheng 252000, China
- 2School of Education Science, Liaocheng University, Liaocheng 252000, China
Abstract
This paper develops an adaptive model predictive control (AMPC) scheme for uncertain nonaffine nonlinear systems by integrating deep Koopman operator theory into a fully data-driven modeling framework. Complex nonlinear systems typically feature prominent nonaffine dynamics and are vulnerable to external disturbances, posing substantial difficulties for controller synthesis. Conventional Koopman-based methods depend on manually designed lifting functions, which suffer from limited modeling accuracy and heavy reliance on prior system knowledge. To address these deficiencies, this work adopts a deep neural network to autonomously learn optimal lifting dictionaries and construct a high-dimensional linear embedding of original nonlinear dynamics. This achieves global system linearization without parametric prior information and converts intractable nonaffine dynamics into a bilinear form amenable to linear control design. On this basis, model predictive control (MPC) is deployed as the core feedback module to guarantee closed-loop stability and satisfy system constraints via real-time receding horizon optimization. Furthermore, an iterative learning control (ILC) strategy is integrated to compensate for system uncertainties and external disturbances. The resulting composite control framework combines the real-time stabilizing merit of MPC and the iterative feedforward refinement capability of ILC across repeated operation trials. Rigorous convergence analysis based on the composite energy function theory verifies the asymptotic zero convergence of tracking errors for repetitive uncertainty components, while bounded residual error exists for non-repetitive disturbances. Comparative simulation results demonstrate that the proposed method effectively reduces modeling and tracking errors while preserving stable closed-loop performance. Quantitative evaluations further validate its superior precision and robustness over existing benchmark approaches, illustrating great applicability to complex nonlinear uncertain systems.
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BibTeX
@article{che2026adaptive,
title = {{Adaptive Model Predictive Control for Uncertain Nonaffine Nonlinear System Based on Deep Koopman Operator}},
author = {Gaofeng Che and Jinchun Deng},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203793},
url = {https://www.mdpi.com/2227-7390/14/20/3793},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Adaptive Model Predictive Control for Uncertain Nonaffine Nonlinear System Based on Deep Koopman Operator
AU - Gaofeng Che
AU - Jinchun Deng
PY - 2026
DA - 2026/10/19
JO - Mathematics
DO - 10.3390/math14203793
UR - https://www.mdpi.com/2227-7390/14/20/3793
AB - This paper develops an adaptive model predictive control (AMPC) scheme for uncertain nonaffine nonlinear systems by integrating deep Koopman operator theory into a fully data-driven modeling framework. Complex nonlinear systems typically feature prominent nonaffine dynamics and are vulnerable to external disturbances, posing substantial difficulties for controller synthesis. Conventional Koopman-based methods depend on manually designed lifting functions, which suffer from limited modeling accuracy and heavy reliance on prior system knowledge. To address these deficiencies, this work adopts a deep neural network to autonomously learn optimal lifting dictionaries and construct a high-dimensional linear embedding of original nonlinear dynamics. This achieves global system linearization without parametric prior information and converts intractable nonaffine dynamics into a bilinear form amenable to linear control design. On this basis, model predictive control (MPC) is deployed as the core feedback module to guarantee closed-loop stability and satisfy system constraints via real-time receding horizon optimization. Furthermore, an iterative learning control (ILC) strategy is integrated to compensate for system uncertainties and external disturbances. The resulting composite control framework combines the real-time stabilizing merit of MPC and the iterative feedforward refinement capability of ILC across repeated operation trials. Rigorous convergence analysis based on the composite energy function theory verifies the asymptotic zero convergence of tracking errors for repetitive uncertainty components, while bounded residual error exists for non-repetitive disturbances. Comparative simulation results demonstrate that the proposed method effectively reduces modeling and tracking errors while preserving stable closed-loop performance. Quantitative evaluations further validate its superior precision and robustness over existing benchmark approaches, illustrating great applicability to complex nonlinear uncertain systems.
SN - 2227-7390
ER -