Tracking Multiple Diffusing Particles Using Information Optimal Control

Abstract

We study the problem of tracking multiple diffusing particles using a laser scanning fluorescence microscope. The goal is to design trajectories for the laser to maximize the information contained in the measured intensity signal about the particles' trajectories. Our approach consists of a two level scheme: in the lower level we use an extremum seeking controller to track a single particle by first seeking it then orbiting around it. In the higher level controller, we decide which particle should be observed at each instant, with the goal of efficiently estimating each particle position while not losing track of any of them. Using simulations, we show that this technique is able to collect photons efficiently and to track multiple particles with low position estimation error.

Real‐Time Feedback‐Driven Single‐Particle Tracking: A Survey and Perspective

“…More recently, an extremum‐seeking controller was developed to converge to an orbit around a fixed fluorescent particle. [ 48,49,138–142 ] Through simulations and experiments, it was shown that this controller naturally switches between two distinct behaviors, converging to the desired orbital motion for slow moving particles and transitioning to a chasing behavior as the speed of the particle increases. While the ability to operate directly on the intensity signal, thereby separating particle localization from control, is appealing, the nonlinear nature of these approaches makes theoretical analysis and parameter tuning more difficult than PID.…”

Real-Time Feedback-Driven Single-Particle Tracking: A Survey and Perspective

“…The controller in this case used a simplex method to measure the photon count rate, and used a gradient ascent to align the laser to the molecule automatically. More recently, an extremum-seeking controller was developed to converge to an orbit around a fixed fluorescent particle [115,20,116,117,21,118,119]. Through simulations and experiments, it was shown that this controller naturally switches between two distinct behaviors, converging to the desired orbital motion for slow moving particles and transitioning to a chasing behavior as the speed of the particle increases.…”