Abstract
In carrying a Brownian particle by means of an external force in one dimension from a place to another in a finite time lapse, we consider controlling the force using a feedback loop to minimize an evaluation functional. The evaluation functional contains the average of the work done to the particle by the force and two terms involving control parameters. One is a term proportional to the mean squared force, while the other is a term proportional to the mean squared distance between the final particle position and the destination. Solving differential equations numerically, we calculate the average work under optimal control for various values of control parameters and find the calculated values bounded from below. The average work is also shown to be larger as we utilize less information on the state of the particle in the feedback control by decreasing the number of observed variables and by increasing the noise amplitude in the observation.
