Fuzzy Multiple Hidden Layer Recurrent Neural Control of Nonlinear System Using Terminal Sliding-Mode Controller

This study designs a fuzzy double hidden layer recurrent neural network (FDHLRNN) controller for a class of nonlinear systems using a terminal sliding-mode control (TSMC). The proposed FDHLRNN is a fully regulated network, which can be simply considered as a combination of a fuzzy neural network (FNN) and a radial basis function neural network (RBF NN) to improve the accuracy of a nonlinear approximation, so it has the advantages of these two neural networks. The main advantage of the proposed new FDHLRNN is that the output values of the FNN and DHLRNN are considered at the same time, and the outer layer feedback is added to increase the dynamic approximation ability. FDHLRNN was designed to approximate the nonlinear sliding-mode equivalent control term to reduce the switching gain. To ensure the best approximation capability and control performance, the proposed FDHLRNN using TSMC is applied for the second-order nonlinear model. Two simulation examples are implemented to verify that the proposed FDHLRNN has faster convergence speed and the FDHLRNN with TSMC has good dynamic property and robustness, and a hardware experimental study with an active power filter proves the feasibility of the method.

I. Introduction

As we all know, most systems in real life are nonlinear mathematical models, containing matching or mismatching unknown disturbances, which make it difficult to control the nonlinear systems. The sliding-mode control (SMC) method has the characteristics of insensitivity to lumped disturbances, and becomes the first choice to design nonlinear controllers [1]–[5]. However, the traditional sliding-mode method selects a linear sliding surface, and the system state only converges to zero when the time approaches infinity. The terminal SMC (TSMC) algorithm has received increasing attention because it can effectively solve the infinite convergence problem. Liu and Sun [6] proposed a typical TSMC method and proved the finite-time convergence of the tracking error. Xu et al. [7] designed a composite neural learning method using a nonsingular TSMC method for a micromechanical system (MEMS) gyroscope. Yu and Man [8] designed a fast TSMC for nonlinear systems. Hussian et al. [9] proposed a finite-time tracking controller for a class of the nonintegral cascade high-order systems. Yang and Yang [10] introduced a nonsingular fast TSMC for nonlinear systems. Divandari et al. [11] designed a speed controller for a switched reluctance motor using fuzzy fast TSMC.