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The variable pump displacement and variable motor speed electro-hydrostatic actuator (EHA), one of the three types of EHAs, has advantages such as short response time, flexible speed regulation, and high efficiency. However, the nonlinearity of its double-input single-output system poses a great challenge for system control. This study proposes a novel EHA with adaptive pump displacement and variable motor speed (EHA-APVM). A closed-loop position is realized using a servomotor. Moreover, the displacement varies with the system pressure; thus, the EHA-APVM is a single-input and single-output system. Firstly, the working principles of the EHA-APVM and the pump used in the system are introduced. Secondly, a nonlinear mathematical model of the proposed EHA-APVM control system is established, and a feedback back-stepping (FBBS) control algorithm is introduced to transform the complex nonlinear system into a linear system on the basis of the back-stepping control theory. Finally, simulation results prove that the EHA-APVM has a quick response and high robustness to variations of the load and the pump displace-ment. In this work, the size and weight of the motor are significantly reduced because the maximum power requirement is reduced, which is very beneficial for using the actuator in airbe equipment.