Gray-Box system modeling using symbolic regression and nonlinear model predictive control of a semibatch polymerization

摘要

A nonlinear model, predictive control approach, based on a gray-box model is introduced in this contribution. The gray-box model is built by combining white-box and black-box modeling elements. The white-box elements consist of relevant mass and energy balances, including algebraic relations that describe different phenomena of the system behavior (e.g., reaction kinetics, heat transfer phenomena, ther-modynamic assumptions). To fill in or compensate for modeling gaps (e.g., missing kinetics information, heat transfer efficiency, inaccurate thermodynamic assumptions), black-box model elements trained from historical process data are introduced into the model. An algorithm for Sparse Identification of Nonlinear Dynamical Systems (SINDy) that identifies the most promising regressors from a pool of possible explanatory functions is used to generate the model's black-box part. The proposed gray-box modeling approach and its application to model predictive control were tested for performance and robustness using a benchmark problem, and the approach shows promising results.