Offset-Free Robust Nonlinear Control Using Data-Driven Model: A Nonlinear Multi-Model Computationally Efficient Approach

TL;DR

This work addresses robustness in nonlinear MPC when data-driven surrogates are used by constructing an offset-free RNMPC framework that embeds an ensemble of compact symbolic-regression NARX surrogates as hard constraints. By capturing epistemic uncertainty at the operating-zone level and enforcing constraint satisfaction across all surrogate models, the approach yields robust performance with low computational cost on a nonlinear ESP system. The study demonstrates that single-zone and multi-zone SR-based RNMPC schemes achieve disturbance rejection and constraint satisfaction, while offering substantial reductions in per-iteration compute time compared with a traditional mechanistic NMPC, and that multi-zone constraint intersections improve safety margins with only modest overhead. These results indicate practical viability for real-time, safety-critical nonlinear control where model uncertainty is prominent and computational budgets are tight.

Abstract

Robust model predictive control (MPC) aims to preserve performance under model-plant mismatch, yet robust formulations for nonlinear MPC (NMPC) with data-driven surrogates remain limited. This work proposes an offset-free robust NMPC scheme based on symbolic regression (SR). Using a compact NARX structure, we identify interpretable surrogate models that explicitly represent epistemic (structural) uncertainty at the operating-zone level, and we enforce robustness by embedding these models as hard constraints. gest margins. The single-zone variant (RNMPC$_{SZ}$) was investigated. Synthetic data were generated within one operating zone to identify SR models that are embedded as constraints, while the nominal predictor remains fixed, and the multi-zone variant (RNMPC$_{MZ}$), zone-specific SR models from multiple operating zones are jointly enforced in the constraint set; at each set-point change, the nominal predictor is re-scheduled to the SR model of the newly active zone. In both cases, robustness is induced by the intersection of the admissible sets defined by the enforced SR models, without modifying the nominal cost or introducing ancillary tube dynamics. The approach was validated on a simulated pilot-scale electric submersible pump (ESP) system with pronounced nonlinearities and dynamically varying safety envelopes (downthrust and upthrust). RNMPC$_{SZ}$ and RNMPC$_{MZ}$ maintained disturbance tracking and rejection, and by intersecting models in the constraints, they increased margins and eliminated violations (especially near the upthrust), with a slight increase in settling time. Including up to four models per zone did not increase the time per iteration, maintaining real-time viability; RNMPC$_{MZ}$ presented the lar

Figures (23)

• Figure 1: Methodology workflow for RNMPC via symbolic regression.
• Figure 2: Illustration of the symbolic regression process implemented by PySRRegressor, showing expression initialisation, evaluation, genetic operations, and model selection through evolutionary optimisation.
• Figure 3: Multi-model RNMPC control strategy incorporating symbolic regression constraints .
• Figure 4: Illustrative layout of the pilot-scale ESP plant.
• Figure 5: Illustrative of single-zone and multi-zone data-acquisition strategies for SR–NARX identification on the ESP operating envelope.