Optimal Control of an Electromechanical Energy Harvester

TL;DR

This paper applies control theory to optimize the electrical resistance in a stochastic energy harvester, improving power extraction by designing time-dependent protocols near the stationary state.

Contribution

It introduces a control-theoretic approach to optimize energy harvesting in stochastic systems by varying electrical resistance over time, a novel application in this context.

Findings

Optimal resistance protocols outperform constant resistance solutions.

Perturbative methods effectively find near-stationary control strategies.

Enhanced power extraction demonstrated through theoretical analysis.

Abstract

Many techniques originally developed in the context of deterministic control theory have been recently 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 in time its controllable parameters 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 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.