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In this paper, adaptive control is presented for a class of single-degree-of-freedom (1DOF) electrostatic microactuator systems which can be actively driven bidirectionally. The control objective is to track a reference trajectory within the air gap without knowledge of the plant parameters. Both full-state feedback and output feedback schemes are developed, the latter being motivated by practical difficulties in measuring velocity of the moving plate. For the full-state feedback scheme, the system is transformed to the parametric strict feedback form, for which adaptive backstepping is performed to achieve asymptotic output tracking. Analogously, the output feedback design involved transformation to the parametric output feedback form, followed by the use of adaptive observer backstepping to achieve asymptotic output tracking. To prevent contact between the movable and fixed electrodes, special barrier functions are employed in Lyapunov synthesis. All closed-loop signals are ensured to be bounded. Extensive simulation studies illustrate the performance of the proposed control.