## 1 Introduction  
Hydraulic servomechanisms have been broadly employed in various industrial applications--e.g., hydraulic robot manipulators [1], hydraulic press [2], load simulators [3], vehicle active suspension systems [4], and so on--due to their superiorities such as a high power-to-weight ratio, fast and smooth response, high stiffness, and ability to generate a tremendous force/torque [5]. However, the inherent highly nonlinear characteristics, parameter variations, modeling uncertainties, and external disturbances of the EHSS are still the major obstacles to achieving high-accuracy tracking performance. Hence, the position tracking problem of the EHSS has attracted many studies in recent years. To control EHSSs, proportional-integral-derivative (PID) control law [6] was initially employed due to its simple structure and easy implementation. However, it is difficult to achieve satisfactory performance since the system dynamics are not compensated in the control law. Alternatively, model-based control strategies for EHSSs such as feedback linearization control (FLC) [7], backstepping control (BC) [8], and adaptive control (ADC) [9] have been widely employed to achieve a better tracking performance. Although in these control methods, the system dynamics are taken into account in control design, they are sensitive to the modeling uncertainties and disturbances that naturally exist in EHSSs. In contrast, SMC [10; 11; 12; 13; 14] which was originally introduced by [PERSON] [15], is considered as a powerful candidate to deal with disturbances and uncertainties, satisfying the matching condition in nonlinear systems that are assumed to be bounded. However, it can be seen that all the above model-based control approaches for EHSSs require the system dynamics to be known, which are complicated and difficult to precisely acquire due to high nonlinearities in pressure dynamics and a number of unknown parameters that need to be identified from experimental input-output data [16]. By virtue of the excellent properties of their self-learning capability and online weight-adaptive mechanisms, radial basis function (RBF) neural networks (NNs) have been employed in various fields such as robot manipulators [17; 18; 19; 20], magnetic levitation systems [21], aircraft [22], hydraulic systems [5; 23; 24; 25; 26], and so on to approximate the unknown dynamic components of control systems. For EHSSs, [PERSON] et al. introduced multilayer RBF NNs to approximate partly mismatched and matched uncertainties [5], and semi-global asymptotic stability was achieved accordingly. In [23], an NN-based estimator was proposed to approximate an unknown term generated in the control design of the hydraulic active suspension systems (ASSs). Besides, an RBF NN-based function approximator [24] was developed to compensate for the effects of the nonlinear friction in EHSSs. In [25], parametric uncertainties and an unknown external load in hydraulic systems were grouped into so-called generalized uncertainties, which were compensated by using RBF NNs. However, in the above-mentioned works, RBF NNs were only exploited to partially approximate model uncertainty in the control system. Hence, the employment of RBF NNs for approximating full model uncertainties is still an open problem. Besides, although RBF NNs are capable of dealing with model uncertainties, they cannot effectively treat disturbances whose behaviors are independent of the system states. Hence, the employment of disturbance observers (DOBs) can be considered as an effective way to cope with disturbances in EHSSs. Extended state observers (ESOs) were employed [27; 28] for EHSSs to estimate both unmeasurable system states and matched/ mismatched disturbances; therefore, high-accuracy tracking performances were achieved. In another approach to cope with disturbances, some DOB designs based on exact differentiators [29] have been applied in hydraulic systems.