## 1 Introduction  
Tracked mobile robots (TMRs) have a wide range of applications in civil, industrial and military fields. However, TMRs are typical nonlinear systems, and it is difficult to perform high-precision trajectory-tracking control [1; 2]. To enhance the control performance of mobile robots, a feasible solution with excellent convergence performance and robustness is imperative in practice. Numerous control methods to address this tracking issue have been reported, including sliding mode control (SMC) [3; 4], backstepping control [5], model predictive control [6], adaptive control [7; 8], etc. In [9], a control method was proposed for a skid-steering mobile robot based on the kinematic control concept and the input-output linearization approach. [PERSON] et al. derived the error dynamics of the path using the combination of the kinematic model of the robot and designed a horizontal steering control law for the path following of the mobile robot [10]. The authors of [11] developed an integer-order prescribed-time controller for a four-wheel independently driven skid-steering mobile robot while considering various disturbances. In recent decades, a new recurrent network, called zeroing neural network (ZNN), has attracted the interest of scholars with its potential for parallel computing and nonlinear processing [12]. The ZNN and its evolved model have been reported to solve robot manipulator quadratic programming [13; 14] and trajectory tracking [15; 16]. [PERSON] et al. proposed a novel supertwisting ZNN to address the tracking control of a robot manipulator [17] which combines SMC and ZNN successfully. [PERSON] et al. developed a ZNN for a bound-constrained omnidirectional mobile robot manipulator by introducing a time-varying non-negative vector [18]. The successful application in robot manipulators motivates us to further explore ZNN application in mobile robots [19], which is a potential field. In [20], a multi-constrained ZNN with the exponential-convergence property was demonstrated by utilizing the time-derivative information, and it was applied to a mobile robot with both performance index optimization and multiple physical-limit constraints. A robust fast-convergence zeroing neural network was proposed in [21] to implement trajectory-tracking application in a noisy environment. A ZNN activated through finite-time-convergence activation was employed for TMR kinematics to track the desired trajectory [22]. The above-mentioned papers about mobile robot trajectory tracking are based on the perspective of kinematic models, which assumes perfect speed tracking [23]. As for an actual situation, the physical parameters of mobile robots, such as mass, inertia, have an impact on system control. Therefore, it is necessary to extend the study of ZNNs to the dynamic level of mobile robots. Moreover, TMRs always work in harsh environments. These papers assume that all the states of the mobile robot are known and accurate and so are the disturbances. However, if the velocity cannot be measured due to sensor faults, the ZNN models proposed above are not viable. Therefore, it is necessary to design a state observer in the ZNN framework to improve the performance of the system. A key feature of an observer is the convergence rate. In a specific situation, there is a great need for rapid convergence of observers to complete the state reconstruction [24]. And some fast-convergence observers have been developed [25; 26; 27]. [PERSON] et al. proposed a fast-finite-time-convergence observer formation control scheme for nonholonomic mobile robots [28]. In [29], [PERSON] presented an observer-based PID for the trajectory-tracking control of wheeled mobile robots with kinematic interferences. However, the upper bound of the settling time is dependent on the initial states for finite-time-convergence observers. In view of this, fixed-time-convergence state observers are explored, which guarantees that the settling time of observer errors is irrelevant with respect to the initial conditions. [PERSON] et al.