Abstract
Many techniques originally developed in the context of deterministic control theory have recently been applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask what is the best way to change its controllable parameters in time in order to maximize, on average, a certain reward function, while steering the system between two pre-assigned states. In this work, we study the problem of optimal control for a wide class of stochastic systems, inspired by a model of an energy harvester. The stochastic noise in this system is due to the mechanical vibrations, while the reward function is the average power extracted from them. We consider the case in which the electrical resistance of the harvester can be changed in time, and we exploit the tools of control theory to work out optimal solutions in a perturbative regime, close to the stationary state. Our results show that it is possible to design protocols that perform better than any possible solution with constant resistance.