Vibration energy harvesting and optimal control theory: an investigation on physical limitations in capturing the environmental energy

Energy harvesting from environment vibration is an important aspect of many technologies. The scale of energy capturing and storage can involve the power range from mwatt up to Mwatt, de- pending on the used devices and the considered environments (from ambient acoustic and vibra- tion, to ocean wave motion). In this paper the energy harvesting problem is reduced to an optimal control problem, where the objective function is the absorption of the maximum amount of energy in a given time interval from a vibrating environment. The interest here is to identify a physical upper bound for this energy storage. The mathematical tool is a new optimal control called Krotov method, that has never been applied to engineering problems, except in quantum dynamics. This approach leads to identify a global maximum in the energy harvesting performances, disclosing limits in the physics of the energy storage form environment vibrations.