In this paper, the stochastic optimal control of a piecewise electromechanically coupled tri-stable energy harvester (TEH) driven by colored noise is investigated. For the purpose of efficient DC supply, the P-SSHI circuit is chosen as the harvesting circuit connected to the TEH. Based on the statistical linearization and the moment method, the analytical expressions of the stationary response moments and the mean harvested power are derived. Then, the stochastic optimal control problem of the TEH is considered from the perspective of extremum optimization of the multivariable function. The effects of colored noise and system parameters on harvesting performance and control effectiveness are further explored. The results show that the time constant ratio can improve the harvested DC power but weaken the rectification efficiency of the circuit, which plays an opposite role to the inversion factor. The electromechanical-coupled coefficient is beneficial to the enhancement of DC power, but it is not conducive to the effectiveness of the control method. The control effectiveness of the rectification efficiency can be optimized by choosing an appropriate noise intensity. The harvesting performance of controlled TEH is significantly higher than that without control. The Monte Carlo simulations (MCS) well support the theoretical results.

Graphical abstract

中文翻译：

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有色噪声下 P-SSHI 电路三稳态能量采集器的随机最优控制

在本文中，研究了由有色噪声驱动的分段机电耦合三稳态能量采集器（TEH）的随机最优控制。为了实现高效的直流供电，选择 P-SSHI 电路作为连接到 TEH 的采集电路。基于统计线性化和矩法，推导了稳态响应矩和平均收获功率的解析表达式。然后，从多变量函数极值优化的角度考虑TEH的随机最优控制问题。进一步探讨了有色噪声和系统参数对收获性能和控制效果的影响。结果表明，时间常数比可以提高收集的直流功率，但会削弱电路的整流效率，其作用与逆变因子相反。机电耦合系数有利于直流功率的增强，但不利于控制方法的有效性。通过选择合适的噪声强度可以优化整流效率的控制效果。受控 TEH 的收获性能显着高于无控制的。蒙特卡罗模拟（MCS）很好地支持了理论结果。

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