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In this paper, an optimal tracking control is designed considering the unknown states for an electro-hydraulic actuator system driven by a proportional directional control valve. Given the practicality of the algorithm, the control voltage applied to the proportional directional control valve satisfies the actuation limits. Furthermore, a discrete Kalman observer is used to overcome the limitation of unmeasured states. The efficacy of the proposed algorithm is verified in simulation as well as in experimental environments. Both simulation and experimental results confirm that the tracking performance of the electro-hydraulic actuator system is improved, and tracking error converges to an arbitrarily small neighbourhood.