## 1 Introduction
In recent years, with the unceasing update and breakthrough of higher control theory, many outstanding scholars in the control field have successively proposed advanced control theories, such as the fuzzy control, artificial neural network (ANN), wavelet neural network (WNN), and self-organizing fuzzy control for nonlinear chaotic systems, switched-reluctance motor drive systems, voice coil motors, and permanent magnet synchronous motors. All have a fairly high reference value. [PERSON] et al. proposed an adaptive recurrent cerebellar model articulation controller for linear ultrasonic motors, which facilitated dynamic performance and faster learning speed for the traditional cerebellar model articulation controller; they used the method of steepest descent to update the dynamic parameters of the controller in real time, thereby achieving the optimal learning velocity such that the tracking error is quickly converged [17]. [PERSON] et al. proposed a wavelet fuzzy neural network that adopts an asymmetric membership function to ameliorate differential evolution algorithms, which are used to control an electric power steering system of a six-phase permanent magnet synchronous motor; it combines the advantages of the wavelet decomposition, fuzzy logic system, and asymmetric membership function [18]. It was developed to realize the control performance and stability required in electric power steering systems. [PERSON] et al. proposed a novel adaptive wavelet fuzzy cerebellar model articulation control system for trajectory tracking control of voice coil motors; this control system includes a wavelet fuzzy cerebellar model articulation controller and a fuzzy compensation controller [19]. Since the wavelet function possessing differential characteristics and fuzzy are adopted, the controller has fast learning ability, due to which it shows significant performance and good tracking characteristics. [PERSON] et al. proposed a sliding-mode control method to be applied on a permanent magnet synchronous motor and added an interference estimator for feed-forward compensation; therefore, the controller possesses good robustness and can use a lower switching gain to ameliorate the chattering phenomenon of the sliding mode [20]. [PERSON] et al. proposed a dynamic Petri-fuzzy cerebellar model articulation controller, which was applied on a magnetic levitation system and a piezoelectric motor drive system; by adding the Petri network, the burden of parameter learning is reduced [20]. [PERSON] et al. proposed a recurrent neural network based on differ ential algorithms and applied it to squirrel-cage induction generators, which can process nonlinear and non-differentiable functions through differential algorithms [20]. [PERSON] et al. proposed a type of function-linked neural network using an asymmetric radial basis function for the three-dimensional motion control of a piezoelectric platform; by using an asymmetric radial basis function, the learning ability of the network can be improved [21]. [PERSON] et al. proposed a type of TSK neural network controller using an asymmetric radial basis function; they used the architecture of functional fuzzy rules to improve the learning rate and applied it to a three-phase grid-connected photovoltaic system [22]. The aim of this research is to develop an adaptive TSK fuzzy self-organizing recurrent cerebellar model articulation controller (ATFSORC) for the synchronization and stability control of chaotic systems. By using ATFSORC, the master and slave systems that are seemingly in a chaotic state can be adjusted according to the reciprocal errors so that the slave system can be synchronized with the master system under different initial conditions. Moreover, TSK fuzzy rules are introduced into a recurrent cerebellar model articulation controller (RCMAC), which is combined with a self-organizing CMAC (SOCMAC) and an improved compensation controller to design the ATFSORC.