## 1 Introduction
Neural networks can learn and approximate any arbitrary nonlinear functions [24]. Therefore, neural networks are implemented to approximate uncertain disturbances in systems as well as to reduce the chattering [25]. A radial basis function (RBF) neural network has several important features such as simple structure, fast learning and better approximation capabilities. It has been adopted in TSM control systems [24; 26]. Wavelet neural networks, which are applied to terminal sliding mode control [27; 28], are a new class of neural networks that have been developed using a combined method of multi-layer artificial neural networks and wavelet analysis. The B-spline function is a piecewise polynomial function widely used in computer-aided design and computer graphics. For its excellent local features, the B-spline function can be used as an activation function of neural network. The B-spline neural networks (BSNNs) can be divided into two groups: one group is based on the B-spline basis function [29; 30; 31; 32] and the other group is based on the B-spline curve [33; 34; 35; 36; 37; 38]. The B-spline basis function is only related to the internal knots, hence the definite internal knots can derive the definite B-spline basis curve. For those kinds of BSNNs, only the weights are trained in some studies [29; 31]. The internal knots are trained by a heuristic algorithm in some other studies [30; 32], making the shapes of B-spline basis function changeable. In this group, the input of the neural network can be considered as the value of internal knots, then according to the b-Spline basis function, the output of the neural network can be obtained. In the group where the B-spline curve is adopted, it is known that the B-spline curve is a linear combination of control points and B-spline basis functions. If the positions of the control points are changed, the shapes of B-spline curves are also changed. In some studies, the weights are considered as control points [38]. Through the training of weights, the BSNN can then become adaptive. In other references, control points are trained by rules. In [33; 37], the position of control points can be changed to a known nearby value, but only one control point can be changed once by this method. Additionally, the input and output of neural network are not relevant directly in this group. In this paper, a novel B-spline neural network with the capability of shape adjustment is proposed and applied to approximate the external disturbance and the unmolded dynamics of the system. The equation of the B-spline curve is reconstructed in numeric form, therefore the new B-spline curve possesses the properties of the radial basis function, making it different from the previous approaches. In this research, the activation function of proposed BSNN is a pp-form spline. The paper is organized as follows: in Section 2, the dynamic model of MSA and the control block diagram are established respectively. Then a new terminal sliding mode control strategy is proposed and proved. In Section 3, a novel BSNN is proposed and the parameter updating rules are built. In Section 4, experiments and simulations are carried out. The performances of the proposed methods are also compared with other methods. Finally, conclusions and contributions are summarized in Section 5.