A Physics-Informed Transformer-Based NMPC Framework for Nonlinear Process Control

Qinyu Bao

doi:10.1109/tii.2026.3734123

A Physics-Informed Transformer-Based NMPC Framework for Nonlinear Process Control

2026-10-08

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DOI：10.1109/tii.2026.3734123

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Industrial nonlinear processes exhibit strong coupling, long-range dependence, and hard constraints, making nonlinear model predictive control (NMPC) suitable for multivariable control. Mechanistic prediction models used in NMPC are costly to develop, sensitive to uncertain parameters, and computationally demanding online; neural-network models represent nonlinear dynamics flexibly but may lose accuracy and extrapolation performance when data are limited. This article develops a physics-informed Transformer (PiTransformer)-based NMPC framework for data-limited nonlinear process control. PiTransformer combines supervised multistep fitting with a physics-informed loss evaluated on unlabeled collocation sequences. A three-stage training scheme progressively introduces physics regularization before the predictor is embedded in terminal-constrained, increment-based NMPC solved online by sequential least-squares programming. Theoretical analysis addresses nominal asymptotic stability and, for sufficiently small bounded model mismatch, local input-to-state stability. The framework is evaluated in two case studies: a nonlinear two-state benchmark and a high-temperature gas-cooled reactor load-following model. In the load-following closed-loop simulation, PiTransformer yields lower tracking errors than NMPC baselines based on a recurrent neural network (RNN), a Transformer, and a physics-informed RNN, and requires an average of 0.11 s per online solve with a 1-s sampling interval. These results support the framework's control effectiveness and real-time feasibility in the tested configuration and provide design guidance for incorporating process knowledge into data-driven NMPC with limited labeled data.

Keywords:

High-temperature gas-cooled reactor (HTGR)

load-following control

nonlinear model predictive control (NMPC)

physics-informed learning

A Physics-Informed Transformer-Based NMPC Framework for Nonlinear Process Control

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