Robust Min–Max MPC with Symbolic Regression Ensembles: Constraint Satisfaction for Uncertain Nonlinear Process Control

Abstract

The control of nonlinear processes with strong dynamic coupling and strict operational constraints is challenging due to the difficulty of developing accurate mechanistic models and the computational cost of solving robust optimization problems in real time. This work proposes a min–max robust nonlinear model predictive control (RNMPC) strategy in which data-driven models obtained through symbolic regression (SR) are integrated as the internal prediction mechanism, forming an ensemble that defines the uncertainty set of the worst-case optimization. The SR models are identified within a nonlinear autoregressive structure with exogenous inputs (NARX) using an evolutionary search algorithm, yielding compact analytical expressions that are differentiable and of low evaluation cost. The methodology was evaluated on an electric submersible pump (ESP) system, which presents strong nonlinearities and tight operational constraints that must be respected at all times. The results demonstrated that the SR-based RNMPC was capable of accurate set point tracking and effective disturbance rejection while maintaining a strictly positive constraint margin across all evaluated scenarios, including tighter operational bounds under which the nominal nonlinear MPC repeatedly operated at the boundary of the admissible envelope. Furthermore, the RNMPC maintained a larger mean constraint margin than the nominal NMPC, confirming the deterministic robustness of the min–max formulation. It is also showed that the compact analytical structure of the SR models allowed the solution time per iteration to be substantially reduced compared to a mechanistic NMPC, confirming the real-time feasibility of the proposed approach for safety-critical process applications.