Automating the task of nanomanipulation is extremely important since it is tedious for humans. This paper proposes an atomic force microscope (AFM) based force controller to push nano particles on the substrates. A block phase correlation-based algorithm is embedded into the controller for the compensation of the thermal drift which is considered as the main external uncertainty during nanomanipulation. Then, the interactive forces and dynamics between the tip and the particle, particle and the substrate are modeled and analyzed. Further, an adaptive critic NN controller based on adaptive dynamic programming algorithm is designed and the task of pushing nano particles is demonstrated. This adaptive critic NN position/force controller utilizes a single NN in order to approximate the cost functional and subsequently the optimal control input is calculated. Finally, the convergence of the states, NN weight estimates and force errors are shown.