## 1 Introduction
Additionally, fixed-time adaptive fault-tolerant control (FTC) techniques were developed specifically for robot manipulators, as highlighted in Ref. [31]. These adaptive control strategies not only ensure fixed-time convergence but also adaptively adjust control parameters to enhance the system's robustness and performance. Through these advancements, robot manipulators can achieve precise and efficient control even in challenging and dynamic environments. Designing a control system for robots poses implementation challenges, as it typically requires knowledge of the robot's dynamic model or at least an upper-bound estimation of the undefined dynamics. To address these challenges, model-free controllers based on learning techniques have been proposed, such as neural networks (NNs) [13; 35; 36] or fuzzy logic systems (FLSs) [31], where learning methods have been widely used in control design to approximate unknown components in robot dynamics. A distributed control using adaptive fuzzy control for autonomous underwater vehicles (AUVs) was developed where FLS is used to approximate the unknown dynamics [29]. For achieving fixed-time stability in adaptive NN-based methods, several solutions have been proposed for robots [37; 38; 39]. Unfortunately, these studies still require the calculation of a part of the robotic system's dynamics. Additionally, in an attempt to achieve overall fixed-time stability, references [38; 39] utilize the conversion constant of the NN instead of estimating its weight. This approach makes it resemble a normal adaptive controller, thereby diminishing the strong properties typically associated with NNs. The prescribed performance control algorithm (PPCA) is a powerful control system design approach that involves specifying measurable outputs for a system and designing a controller to achieve the desired performance [13; 40; 41]. This approach is particularly useful in complex or uncertain systems where traditional control techniques may fall short. By prescribing the desired performance directly, the PPCA can offer increased robustness to uncertainties and disturbances, resulting in better overall performance. However, it is important to recognize that the PPCA does have limitations. For example, the system's performance can be sensitive to changes in system dynamics or operating conditions, and the accuracy of the system model is crucial for achieving desired performance. Inaddition, some studies have pointed out potential singularity issues with certain used ETFs [39; 40; 42; 43]. Therefore, to maximize its capabilities, the PPCA should be combined with other control methods. After a thorough analysis of the challenges in controlling robot manipulators, we developed a novel control system with global fixed-time stability for robots. The proposed approach utilizes a fixed-time adaptive NN controller designed within TSMC and the PPCA framework to achieve global convergence of the controller in a fixed time, following Lyapunov criteria. This paper contributes in several ways:  
* Our approach uses two separate pre-specified performance functions (PPFs) to set bounds for tracking errors. One PPF limits the convergence rate and steady-state error, while the other addresses overshoot and the steady-state error. This enlarges the performance space at a steady state compared to traditional methods. Additionally, the symmetric steady-state error boundaries ensure the zero-tracking error when the transformed error is zero, simplifying the ETF design.