Adaptive multilayer T-S fuzzy controller for nonlinear SISO system optimized by differential evolution algorithm

Abstract

In this paper, the authors propose a novel adaptive multilayer T-S fuzzy controller (AMTFC) with an optimized soft computing algorithm for a class of robust control uncertain nonlinear SISO systems. First, a new multilayer T-S fuzzy was created by combined multiple simple T-S fuzzy models with a sum function in the output. The multi-layer fuzzy model used in nonlinear identification has many advantages over conventional fuzzy models, but it cannot be created by the writer's experience or the trial and error method. It can only be created using an optimization algorithm. Then the parameters of the multilayer fuzzy model are optimized by the differential evolution DE algorithm is used to offline identify the nonlinear inverse system with uncertain parameters. The trained model was validated by a different dataset from the training dataset to guarantee the convergence of the training algorithm. Second, for robustly and adaptive purposes, the authors have proposed an additional adaptive fuzzy model based on Lyapunov stability theory combined with the optimized multilayer fuzzy. The adaptive fuzzy based on the sliding mode surface is designed to guarantee that the closed-loop system is asymptotically stable has been proved base on a Lyapunov stability theory. Furthermore, simulation tests are performed in the Matlab/Simulink environment that controlling a water level of a coupled tank with uncertain parameters are given to illustrate the effectiveness of the proposed control scheme. The proposed control algorithm is implemented in simulation with many different control parameters, and it is also compared with the conventional adaptive control algorithm and inverse controller. The simulation results also show the superior of the proposed controller than an adaptive fuzzy control or inverse controller when using the least mean square error standard.