## 1 Introduction
Like k-NN, CART methods do not manipulate the input data during training, and in cases of overlapping feature spaces, the classification performance of the decision trees can be poor. During the training stage, ANNs may neglect some data problems while adjusting the weights andhyperparameters. However, ANNs have some limitations, such as gradient pitfalls and longer training times for large data sets that may not allow for an optimal solution. To avoid these issues and to address the problem of fault diagnosis, the support vector machines (SVMs) [20; 21; 22; 23] machine learning algorithm is utilized in this paper. This algorithm has a strong mathematical background, and better addresses feature dimensionality due to the availability of the different types of kernels that can be used for training. For this paper, a linear kernel [24] was chosen as the kernel function due to the small number of extracted features and the linear separability of the available data. To extend the capabilities of SVM and solve the multiclass classification problem, a \"one-against-one\" [25] strategy was employed for training. Numerous procedures have been introduced for fault-tolerant control (FC). These strategies are classified into two groups: a) active fault-tolerant control and b) passive fault-tolerant control [3]. The active fault-tolerant control includes two steps. First, the fault is detected and identified. Then, the effect of the fault is reduced. In the passive fault-tolerant control, the impact of the fault is decreased directly based on control techniques [10]. In this investigation, active fault-tolerant control is adopted for fault-tolerant control in the robot manipulator. The active fault-tolerant control is classified into two main groups: a) linear and b) nonlinear. Linear procedures lead to unsatisfactory fault-tolerant control due to coupling effects parameters, noisy conditions, and increased gear. To address these issues, the use of a nonlinear fault-tolerant controller is suggested. Various nonlinear active fault-tolerant controllers have been presented in the literature, including model-based [3], artificial intelligence-based [26] and hybrid [10]. The model-based active fault-tolerant controllers have numerous advantages, such as stability, robustness and reliability, but its performance under unknown conditions is the main argument against its use. To address this weakness, artificial intelligence-based and hybrid controllers can be used. However, artificial intelligent active fault-tolerant controllers procedures have many issues concerning robustness and reliability. To address the faults in model-based and artificial intelligence, a hybrid fault-tolerant controller was presented in [10]. Various hybrid algorithms have been defined for fault-tolerant control in robot manipulators, such as the modern fuzzy feedback linearization technique [8], fuzzy sliding mode controller [10] and neuro sliding mode approach [27]. In this research, the adaptive modern (adaptive neuro observation) fuzzy backstepping variable structure controller is selected for fault-tolerant control of a robot manipulator. A variable structure controller (VSC) is a robust and reliable model-based technique, and is one of the most suitable candidates for fault-tolerant control of robot manipulators. Three basic problems must be addressed: (a) the chattering phenomenon, (b) the system's dynamic dependency and c) robustness in faulty conditions [3]. Based on the literature, to decrease chattering, multiple procedures, such as the boundary layer method, sliding mode fuzzy technique, and PID sliding mode control algorithm, have been devised [10]. Similarly, the robustness of a VSC can be improved using the adaptive techniques reported in [10]. Therefore, to improve robustness and reduce high-frequency oscillations (chattering phenomenon) under faulty conditions, the backstepping algorithm is used in parallel with the VSC to design a BVSC.