## 1 Introduction  
With the development of modern forklift technology, handling stability and active safety are becoming increasingly important. Forklift sensors of yaw rate, sideslip angle, and roll rate are used to measure dynamic characteristics of a forklift. Deviation of these sensors' signals may lead to spurious triggering or misoperation of the control system. Once a fault occurs, it causes serious consequences [1; 2; 3], so the possibility to diagnose and reconstruct potential faults of these sensors is the key issue of safety and stability of a forklift. To detect an incipient fault as early as possible to avoid serious damage to the controlled system, a fuzzy relational sliding mode observer (FRSMO) is proposed [4]. In recent years, different types of observers have been used for sensor fault detection and reconstruction. A sliding mode observer (SMO) is commonly used as a robust control solution for mode errors and measurement disturbances. For a class of uncertain time-delay systems, a robust SMO, which guarantees estimation error stability through the Lyapunov--Krasovskii function and the Linear Matrix Inequality (LMI) optimization, has been proposed [5; 6]. An SMO with two discontinuous terms was designed to compensate for fault behavior and disturbance variation from the system state estimation. It ensured robust fault reconstruction and estimation for a class of nonlinear systems described by the Takagi-Sugeno model with unmeasurable premise variables subject to the faults affecting actuators, sensor faults, and unknown disturbances [7]. In this study, an SMO with adaptive regulation law is proposed. It establishes a linear state equation with output disturbance to convert sensor faults into actuator faults. [PERSON] et al. also transformed sensor faults into actuator faults by introducing a new state variable [8]. By considering the sensor fault and output disturbance as auxiliary state vectors, a robust sliding mode descriptorobserver is discussed for estimating states and reconstructing actuator and sensor faults simultaneously in the presence of uncertainties, measurement noise, and output disturbances [9; 10]. For practical application in engineering, a neural adaptive observer has been developed to detect faults in sensors and actuators of unmanned aerial vehicle (UAV) systems. In the design, weighting parameters of the Neural Network (NN) were updated by using the Extended Kalman Filter (EKF). The proposed fault detection strategy was applied to a nonlinear dynamic model of UAV for evaluation [11]. [PERSON] et al. also dealt with the embedded fault detection and isolation (FDI) / fault-tolerant control approach applied to an over-actuated electric vehicle [12]. A new scheme based on a nonlinear dynamic model is also designed for sensor fault detection and isolation (FDI) in a UAV system. In the proposed design, the NN is used as an observer for faults of UAV sensors, and weighting parameters of the NN are updated by using the EKF [13]. Fault-tolerant control (FTC) for vehicle Steer-by-Wire (SBW) systems in the presence of an actuator fault and bounded uncertainties has been proposed. A fault observer was developed to assess fault information and faulty SBW systems. The minimax model predictive control in the delta domain was deployed to achieve tracking performance in the event of an actuator fault, system uncertainties, and disturbances [14; 15]. [PERSON] et al. focused on single and multiple current FDI sensors for induction motor drives in an electric vehicle; two models based on diagnostic methods were proposed; the first one was a differential algebraic estimation of fault dynamics and the second one was based on a combination of the Robust Integral Sign of the Error observer [16]. [PERSON] et al. investigated the adaptive FTC and fault reconstruction problem for autonomous underwater vehicles (AUVs) subject to ocean current disturbance and modeling uncertainty [17].