## 1 Introduction
For example, a linear disturbance observer (LDOB) [30] for hydraulic rotary actuator (HRA) control systems and nonlinear disturbance observers (NDOBs) [1; 31] for hydraulic robot manipulators have been successfully employed to actively reject the influence of the grouped disturbances on the tracking performance. It is noted that the above-mentioned DOB designs require the construction of an observer with a careful tuning process of observer gains to achieve highly efficient disturbance compensation. Hence, to simplify the parameter tuning, the unknown disturbance estimator (UDE) [32] has been proposed with only one parameter that needs to be selected. Nevertheless, similar to model-based control approaches, DOB designs require system dynamic information, which inhibits the applications of DOBs. In addition, the employment of RBF-NNs and DOBs to cope with partial uncertainties and disturbances has been studied [33; 34]. However, to the best of the authors' knowledge, the integration of RBF NNs and DOBs into a controller to treat the problem of full model uncertainties and disturbances is still challenging, and this is considered in this paper. Motivated by the above comprehensive analysis, in this paper, a novel adaptive robust control mechanism for the EHSS with completely unknown dynamics and disturbances is originally proposed. In this framework, high-order sliding mode exact differentiators [35] are adopted to exactly calculate the angular velocity, acceleration, and pressure derivative. Based on that, all unknown dynamic functions in system dynamics are approximated by RBF-NN-based approximators. For the first time, a pair of NN-based DOBs is established to estimate and compensate for the effects of the NN approximation imperfections, unmodeled dynamics, and external load on the control system of the EHSS simultaneously. Finally, the full-state feedback robust control law is synthesized to ensure the high-accuracy tracking performance in the presence of completely unknown dynamic functions and both matched/mismatched lumped disturbances. The overall system stability is proven by utilizing the Lyapunov theory. Several simulations are conducted to verify the effectiveness of the proposed control strategy. The main contributions of this paper are summarized as follows:1. The RBF NN-based function approximators with adaptive mechanisms are designed to online approximate all unknown dynamic functions in the dynamics of the EHSS. 2. A pair of DOBs based on the HOSM differentiators along with NNs are first developed to effectively estimate and actively compensate for not only the effects of both mismatched and matched disturbances but also the imperfections of the function approximation of RBF NNs. 3. A robust control law based on the RBF NNs and DOBs is synthesized to guarantee the high-accuracy tracking performance of the EHSS control system under the impacts of large model uncertainties and disturbances. 4. The combination of RBF NNs and DOBs in order to take all their advantages is originally introduced to efficiently treat both full model uncertainties and disturbances in the dynamics of EHSSs. The remainder of the paper is organized as follows. In Section 2, the system modeling is presented. The high-order differentiator, neural network-based system dynamic approximators, disturbance observers, and control strategy are developed in Section 3. The total system stability is analyzed in Section 4 and comparative numerical simulations are conducted in Section 5. Finally, Section 6 concludes this paper.