Non-vector space stochastic control for nano robotic manipulations

In this paper, we present a non-vector space stochastic control method for nano robotic manipulations. Non-vector space control employs sets as the states and formulates dynamics equations in the space of sets. This method provides a natural description of physical phenomena such as images. When applied to nanomanipulations, it excludes the use of external position sensors, and the positioning precision can be as good as the imaging resolution. In this paper, we investigate the stochastic control problem for non-vector space dynamic systems when the sets are corrupted by random noises. We use Kalman filtering to estimate the true set for feedback control. The stability of the method is investigated. We apply the method to atomic force microscope (AFM) system to improve position accuracies of nanomanipulations. Simulation and experimental results have clearly validated the proposed method.