## 1 Introduction
Further, to address the system's dynamic dependency, the proportional-integral-derivative (PID) fuzzy technique is used along with a BVSC to design an FBVSC. To design a PID fuzzy controller with a minimum rule-base, the PD-fuzzy-plus-PI-fuzzy algorithm is used. To allow for fault modification in the controllers, the active fault-tolerant control is suggested. Thus, the proposed neural adaptive observer (ANHVSO) is applied to the FBVSC to design a modern FBVSC (MFBVSC). Furthermore, to increase robustness and decrease chattering, the adaptive technique is used to fine-tune the variable structure parameters in faulty conditions. The adaptive MFBVSC (AMFBVSC) is used to reduce the effects of faults in the robot manipulator. Figure 1 shows a block diagram of the SVM-based neural adaptive, high-order variable structure observer fault diagnosis and fault-tolerant control for a robot manipulator. The diagram has four main parts: (a) modeling the dynamic behavior of the robot manipulator based on the Lagrange technique [28], (b) estimation of the normal and abnormal signals based on the neural adaptive high-order variable structure observer, (c) detection and identification of faults based on the machine learning (SVM)  
algorithm, and (d) fault-tolerant control of the robot manipulator using an adaptive modern (neural adaptive high-order variable structure observer) fuzzy backstepping variable structure controller. Figure 1: Block diagram of the Support Vector Machine (SVM)-based adaptive neuro variable structure observer fault diagnosis and fault-tolerant control of robot manipulator. Estimating normal and abnormal signals based on the neural adaptive high-order variable structure observer has four principal sub-blocks: (i) designing the variable structure observer (VSO), (ii) implementing a high-order VSO to reduce chattering, and evaluating it using the super-twisting method, (iii) evaluating the accuracy of the high-order super-twisting VSO (HVSO) using a neural-network technique, and (iv) improving the reliability and robustness of the neural higher-order super-twisting variable structure observer (NVSO) using the adaptive approach. Detection and identification of faults based on the support vector machine (SVM) algorithm has three main sub-blocks: (i) generation of the residual signal based on the difference between the original and estimated signals, (ii) characterization of windows by the energy feature for position and torque signals, and (iii) the detection and classification of the fault types using the SVM technique. Fault-tolerant control of the robot manipulator using the adaptive, modern (ANHVSO), fuzzy, backstepping variable structure controller has five main sub-blocks: (i) the variable structure controller (VSC) is designed, (ii) a backstepping control algorithm to reduce chattering is expressed and evaluated using a backstepping variable structure controller (BVSC), (iii) the difficulty of determining a system's BVSC dynamics under uncertain conditions is evaluated using a fuzzy procedure, (iv) the accuracy and extent of fault-tolerance in the fuzzy BVSC (FBVSC) is evaluated using a modern (ANHVSO) approach, and (v) the robustness and reliability of the fault-tolerant controller in the modern FBVSC (MFBVSC) is improved using an adaptive procedure. The main contributions of this research can be summarized as follows:  
1. Improved estimation accuracy of normal and abnormal signals based on the neural adaptive, high-order, variable structure observer. 2. Implementation of the SVM-based neural adaptive, high-order, variable structure observer to improve fault detection and identification accuracy in a robot manipulator. 3. Improvement of the fault-tolerant control in the fuzzy variable structure controller of a robot manipulator using three important algorithms: (a) backstepping control technique, (b) neural adaptive high-order variable structure observer and (c) an adaptive technique. The rest of this research paper is organized as follows.