Optimal control of a laser source to generate a minimum time trajectory of a droplet in a liquid layer

This paper describes the use of optimal control theory applied to the motion of a low-power laser beam to precisely move a droplet in a liquid layer by means of the force on the liquid-liquid interface arising due to the surrounding thermal field (thermocapillary force and Marangoni effect). The form of heat field equations is approximated by the solution of a finite sum of laser pulses, whose analytical solution can be explicitly derived. In this way, the model of the system does not contain any partial differential equation (PDE). Optimization is performed by using the direct approach method and the fmincon solver provided by Matlab. The initial guess is found with a simple model predictive controller. Perspective applications of this technology include beam-controlled targeting of pharmaceuticals in organic tissues.