Stochastic optimal control of a coupled tri-stable energy harvester under correlated colored noises

In this paper, the stochastic optimal control of a tri-stable energy harvester (TEH) under a standard rectifier circuit driven by correlated colored noises is considered. From the view of physical intuition, the control force is directly separated into conservative component and dissipative one. Then, the stationary probability density function (SPDF) and the DC power of the controlled electromechanical coupled TEH can be derived by using the stochastic averaging based on energy-dependent frequency. The weighted combination of mean DC power and rectification efficiency is regarded as a performance index to transform the stochastic optimal control problem into an extremum problem of a multivariable function. The stochastic direct optimal control strategy developed in this paper avoids the trouble of dealing with complex differential equations. In contrast with the uncontrolled case, the TEH under direct optimal control achieves significant optimization of harvesting performance. The cross-correlation between the additive and multiplicative colored noises can break the symmetry of SPDF to induce random transition. The power conversion efficiency of the harvesting system can be optimized by choosing the appropriate noise intensities.