Tracking Multiple Diffusing Particles Using Information Optimal Control

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.