## 1 Introduction  
In recent years, robot manipulators have been rapidly developing in many applications that require high accuracy in tracking performance. However, up to now, formulating controllers satisfying control performance and the stability of the system is still a big challenge due to its high nonlinearity, coupling dynamics reactions, and uncertainties [1]. In order to deal with these problems, many approaches such as using a proportional integral derivative (PID) control [2], feedback linearization [3], robust control [4; 5], adaptive control [6; 7; 8], backstepping (BSP) control [9; 10], hybrid proportional derivative sliding mode control (PDSMC) [11], sliding mode control (SMC) [12; 13; 14; 15] and even intelligent control [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31] have been studied. Sliding mode control (SMC) is known as one of the most feasible solutions with fast response and strong robustness to resolve perturbation such as external disturbances, or unmodeled blocks in nonlinear systems compared with traditional methods [14; 15]. When precise control is considered as an important criterion, the adaptive algorithm needs to be constructed rigorously. [PERSON] et al. [16] formulated an adaptive fuzzy sliding mode control (AFSMC) using a supervisory fuzzy control where a fuzzy logic system (FLS) was employed to replace switching terms and switching gain in the robust control signal of the SMC. [PERSON] et al. [17] integrated adaptive laws to determine the parameters of the FLS and then used FLS to approximate switching gains and eliminate the chattering. The FLS, whose laws were designed based on some knowledge about the control system [18], has been successfully applied to many linear and non-linear systems [19; 20]. In such studies, the FLS with adaptive laws were employed to adjust controller gains of the SMC. The adjusted gains for the controller were chosen based on trial-and-error methods and experiments to determine suitable values. Those results indicated that the tracking performance could be improved. However, as mentioned above, the FLS was set up based on the knowledge of the system dynamics and experience of designers, which is difficult to carry out in practice, and the matrix of fuzzy rules is complicated to design [21]. Neural network control (NN) has been successfully used in many commercial and industrial applications in recent years [21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. In those studies, the NN is used as a compensator or an approximator to boost or enhance the control signal, compensate uncertainties, or eliminate disturbances. [PERSON] et al. employed the NN to observe the velocity of links and then combined with an adaptive law and SMC to compensate for errors and disturbance [22]. [PERSON] et al. used radial basis function (RBF) NN to estimate system dynamics and compensate approximation errors as well [23]. [PERSON] proposed a reference compensation technique (RCT) where the NN was constructed to compensate uncertainties at the trajectory level [24; 25]. [PERSON] et al. proposed the radial basis function neural network (RBFNN) to approximate unknown robot function [26]. [PERSON] et al. utilized RBFNN to control the position of a piezo positioning stage [27]. [PERSON] et al. proposed a robust adaptive control method based on a dynamic structure fuzzy wavelet neural network (FWNNs) system for trajectory tracking control of industrial robot manipulators to compensate for structured and unstructured uncertainties and to model complex processes [28]. These results indicated that the tracking performance was improved compared with the conventional technique. Besides that, the NN technique can be used to directly adjust the controller to adapt to the system dynamics. Some approaches utilized this technique for adjusting the controller gains to achieve higher performance [21; 29; 30; 31]. [PERSON] et al.