# Adaptive Fuzzy Command Filtered Tracking Control for Flexible Robotic Arm with Input Dead-Zone
## 1 Introduction
However, the use of these filters leads to filtering errors, affecting control precision [21]. In order to mitigate these errors, researchers have suggested the adoption of command filtering techniques and the introduction of compensation signals. The authors of [21; 22] successfully utilized command filtering techniques to address computational explosion problems and eliminate filtering errors, resulting in improved control precision. In the context of addressing robotic arm control challenges, various innovative approaches have been proposed. For example, [PERSON] et al. [23] introduced a novel adaptive fuzzy neural network control method to address the trajectory tracking control of robotic arms with output constraints and nonlinear inputs. Meanwhile, [PERSON] et al. [24] explored an adaptive fuzzy sliding mode robust control algorithm to address trajectory tracking control for robotic arms in the presence of uncertain parameters and external disturbances. On a different note, [PERSON] et al. [25] presented an adaptive sliding mode control method to resolve robotic arm tracking control issues involving unknown external disturbances. [PERSON] et al. [26] introduced an adaptive fault-tolerant control strategy to handle actuator failures and uncertain boundary disturbances, achieving the control of robotic arms. [PERSON] et al. [27] investigated a fault-tolerant control design to effectively control robotic arms in the presence of actuator failures, input saturation, and external disturbances. [PERSON] et al. [28] proposed an adaptive sliding mode control approach to address the issue of oscillations in control torque and verified the effectiveness of this control method through simulations. However, these methods require the measurement of velocity and angular displacement within the robotic arm system. Yet, in practical engineering scenarios, considering factors like the cost and size of the robotic arm, velocity sensors are often omitted, resulting in certain states being unmeasurable. When aiming to achieve more precise robotic arm control, it is necessary to obtain various states of the system during its operation. Therefore, designing an effective observer is of significant importance for the state estimation of a robotic arm with unobservable states. Furthermore, the various random disturbances present during the operation of robotic arm systems also constitute a significant influencing factor on system stability [29]. Researchers have conducted in-depth studies on issues such as actuator saturation, friction constraints, and external disturbances [30; 31; 32]. It is worth noting that dead-zone inputs, as a type of nonlinear non-smooth problem [33; 34; 35], frequently arise in industrial processes. However, the effects stemming from dead-zones are often overlooked for the convenience of controller design. If the dead-zone issue is not addressed, it can lead to discontinuities in the system's response, resulting in instability and performance degradation near the dead-zone region. In practical operations, the inadequate resolution of the dead-zone problem can prevent the system from achieving expected performance and may even induce instability and accidents. Therefore, it is important to consider dead-zone issues in the design of control systems. However, there is limited research on flexible robotic arm systems with dead-zone inputs, and there are scarce outcomes concerning adaptive fuzzy command filter control for such systems. This motivated us to conduct this study. Additionally, we also conducted research on systems with unobservable states based on the above discussions. This paper proposes an adaptive fuzzy state feedback control method to achieve trajectory tracking in flexible robotic arm systems, taking into account the presence of dead-zones and unobservable states. The method utilizes a fuzzy logic system to approximate nonlinear functions and a state observer to estimate unobservable states in nonlinear systems.