随机Rayleigh振子瞬态响应及其最优控制

Optimal Control of Transient Response of Stochastic Rayleigh Oscillator

研究了随机Rayleigh振子瞬态响应极最优控制问题。利用随机平均法得到原系统振幅部分平均随机Ito方程。控制力有界,由Bellman动态规划原理得最优控制率,进而推导出系统振幅完全平均Ito方程和相应Fokker-Planck-Kolmogorov方程。基于退化线性系统得到正交基空间,在此空间上应用Galerkin方法得到近似瞬态响应。计算结果表明该方法求解受最优控制力作用的随机非线性系统瞬态响应非常有效且求解效率远远高于Monte-Carlo数值模拟。

The stochastic optimal bounded control of the transient response of stochastic Rayleigh oscillator. First is studied, the stochastic averaging method is adopted to obtain the partly averaged stochastic It6 equation for the amplitude of the original system. Secondly, the Bellman dynamic programming principle is carried out to obtain the stochastic optimal bounded control strategy. Thirdly, the totally completed It6 equation is obtained. The corre- sponding Fokker-Planck-Kolmogorov equation is obtained. Applying Galerkin procedure to the Fokker-Planck-Kol- mogorov equation, an approximate solution is derived. The Monte-Carlo simulation is applied to the original sys- tem. The results obtained from the theory solutions and the digital solutions together show the accuracy and the ef- fectiveness of the proposed procedure.