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Considering the non-affine-in-control system governing the motion of a spherical particle trapped inside an optical 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 framework in the presence of external disturbances and initial bead positions that are located far away from the laser beam. 

This paper investigates the problem of prediction of protein molecule folding pathways under entropy-loss constraints by formulating a control synthesis problem whose solutions are obtained by solving large-scale quadratic programming (QP) optimizations with nonlinear constraints. The utilized non-iterative and computationally efficient algorithm, which is based on solving generalized eigenvalue problems, prevents an unpredictable and potentially large number of iterations at each protein conformation for computing the folding control inputs. The synthesized control inputs remain close to the renowned kinetostatic compliance method (KCM) reference vector field while satisfying proper quadratic inequality constraints that limit the rate of molecule entropy-loss during folding.