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The dual heuristic programming (DHP) approach has a superior capability to solve approximate dynamic programming problems in the family of adaptive critic designs (ACDs). In this paper, a DHP based controller is developed for vibration isolation applications. In the specific case of an active-passive isolator, a multilayer feedforward neural network is pre- trained as a differentiable model of the plant for the adaptation of the critic and action networks. In addition, in order to avoid plunging in the local minima during the training process, pseudorandom signals, which represent the vibrations of the base, are applied to the vibration isolation system. This technique greatly improves the robustness of the DHP controller against unknown disturbances. Moreover, the "shadow critic" training strategy is adopted to improve the convergence rate of the training. Simulation results have shown that the developed DHP controller alleviates vibration disturbances more effectively and have better control performance in comparison with the passive isolator. Additionally, as compared with the one adapted on-line, the pre-trained model network leads the training to be more efficient. Therefore, it further demonstrates the effectiveness of the DHP controller designed with the pre-trained model network even in the presence of unmodeled uncertainties.