A Control Lyapunov Function-Based Approach for Particle Nanomanipulation via Optical Tweezers

Considering the non-affine-in-control system gov- erning the motion of a spherical particle trapped inside an opti- cal tweezer, this paper investigates the problem of stabilization of the particle position at the origin through a control Lyapunov function (CLF) framework. The proposed CLF framework enables nonlinear optimization-based closed-loop control of position of tiny beads using optical tweezers and serves as a first step towards design of effective control algorithms for nanomanipulation of biomolecules. After deriving necessary and sufficient conditions for having smooth uniform CLFs for the optical tweezer control system under study, we present a static nonlinear programming problem (NLP) for generation of robustly stabilizing feedback control inputs. Furthermore, the NLP can be solved in real-time with no need for running computationally demanding algorithms. Numerical simulations demonstrate the effectiveness of the proposed control frame- work in the presence of external disturbances and initial bead positions that are located far away from the laser beam.