Stochastic control for nanoparticle manipulation using electric fields

Abstract

A simplified model is used to study the dynamics of a nanoparticle suspended in a fluid under Dielectrophoretic (DEP) force. The model considers the DEP force (considering only dipoles formed and not higher order polarisation) and the Brownian motion of the particle. Stochastic control and estimation methods are introduced to provide control action via DEP force that pushes the particle in a specific direction. The control action employed is based on alternating the polarity of the electric field that induces the force exerted on the particle. Despite the simplicity of the model, a sufficient insight into the nature of applying stochastic control techniques can be derived. Simulations are also presented to illustrate the proposed stochastic control techniques, by simulating the behaviour of the controlled nanoparticle system described by a stochastic differential equation driven by Brownian motion subject to optimal DEP force computed by solving an optimal stochastic control problem.