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A novel reinforcement learning-based neural network (RLNN) controller is presented for the manipulation and handling of micro-scale objects in a micro-electromechanical system (MEMS). In MEMS, adhesive, surface tension, friction and van der Waals forces are dominant. Moreover, these forces are typically unknown. The RLNN controller consists of an action NN for compensating the unknown system dynamics, and a critic NN to tune the weights of the action NN. Using the Lyapunov approach, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error and weight estimates are shown by using a novel weight updates. Simulation results are presented to substantiate the theoretical conclusions.