受宽带随机激励的最优反馈控制

Feedback control optimization for stochastic dynamic systems under wide-band random excitations

文章提出了基于平稳响应的随机最优反馈控制策略,研究了受宽带随机激励的Hamilton系统的最优反馈控制。首先应用拟Hamilton系统随机平均法建立平均后的Ito∧随机微分方程;接着求解相应的Fokker-Plank-Kol-mogorov(FPK)方程得到系统精确平稳解;然后将控制力的均方值和Hamilton能量均值结合作为系统控制指标,得出最优反馈控制规律;最后用两个例子详细说明了这一控制方法的实施过程的有效性,数字模拟结果与理论结果完全吻合。

A strategy of feedback control optimization of stochastic dynamic systems via stationary response is proposed. First, the control system subjected to wide-hand random excitations is formulated based on the stochastic averaging method for quasi-integrable Hamiltonlan systems and then transformed into Ito stochastic differential equation. Second, the averaged Ito stochastic differential equation for the system is derived and the stationary solution of the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation is obtained. Third, the mean square value of the control force and the Hamiltonian function are combined handily as the performance index of the system and the optimal control force is obtained. Finally, two examples are worked out in detail to illustrate the application and the effectiveness of the proposed strategy.