Nonlinear System Identification Using Takagi-Sugeno Multi-model: Optimization via Grey Wolf and Levenberg-Marquardt Algorithm with Application to the Monod System

Abstract

This paper introduces a novel approach for modeling nonlinear systems using a coupled multi-model framework, specifically based on Takagi-Sugeno models. The proposed method relies on system identification through input-output data, treating the nonlinear system as a black box. Multi-model parameters are derived by minimizing a quadratic criterion that quantifies the difference between the outputs of the nonlinear system and the multimodel. This optimization is carried out using the iterative Levenberg-Marquardt algorithm. To address the convergence and divergence issues common in iterative algorithms due to initial parameter sensitivity, the Grey Wolf Optimizer (GWO) is employed to enhance the optimization process. The GWO-derived parameters are then used as initial values for the Levenberg-Marquardt algorithm, ensuring improved convergence. The proposed method’s performance is validated through its application to the Monod system, with results demonstrating its effectiveness and accuracy.