GA-Based Binary Sparse Data-Driven Identification and Nonlinear Model Predictive Control of Diesel Engine Air-Path System

Abstract

This research is on the sparse identification of nonlinear dynamic systems (SINDy) for the modeling of a diesel engine air-path system and its use in the nonlinear model predictive control (NLMPC) of the air-path system. The proposed modeling strategy involves a binary optimization scheme based on genetic algorithm (GA) to promote model accuracy and sparsity. Prior studies have demonstrated the applicability of SINDy-based modeling using conventional sequentially thresholded least-squares (STLSQ) method for a diesel engine air-path system. This air-path system is a nonlinear multi-input multi-output (MIMO) system of high degree. However, the modeling accuracy achieved by conventional STLSQ-based approach has been limited, particularly when the library is added with nonlinear terms of higher order. Therefore, this research proposes a new data-driven model discovery approach based on GA-based binary optimization and STLSQ with multiple thresholds, referred to as Binary-STLSQ-MT, to overcome the above limitations. As a result, Binary-STLSQ-MT successfully identified models using the library that include higher order terms, for which conventional STLSQ tends to suffer from numerical instability or divergence. It also achieved a higher coefficient of determination than the conventional approach, with approximately 2% improvement for ${{y}_1}$. Furthermore, when applied to NLMPC, the model identified by Binary-STLSQ-MT achieved superior control performance, reducing the NLMPC objective function values by approximately 57% compared with the conventional STLSQ-based model. These findings indicate that the proposed modeling approach substantially extends the practical applicability of SINDy to realistic nonlinear MIMO control problems.