| 随机Rayleigh振子瞬态响应及其最优控制 |
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| 引用本文： | 戚鲁媛,徐伟,高维廷. 随机Rayleigh振子瞬态响应及其最优控制[J]. 科学技术与工程, 2013, 13(4) |
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| 作者姓名： | 戚鲁媛 徐伟 高维廷 |
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| 作者单位： | 西北工业大学理学院应用数学系,西北工业大学理学院应用数学系,西北工业大学电子信息学院 |
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| 基金项目： | 国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 摘 要： | 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It?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It?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。
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| 关 键 词： | 色噪声，最优有界控制，Galerkin法，Monte-Carlo模拟，随机平均法 |
| 收稿时间： | 2012-09-06 |
| 修稿时间： | 2012-09-06 |
Optimal control of transient response of stochastic Rayleigh oscillator |
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| Qiluyuan,and. Optimal control of transient response of stochastic Rayleigh oscillator[J]. Science Technology and Engineering, 2013, 13(4) |
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| Authors: | Qiluyuan and |
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| Abstract: | This paper studied the stochastic optimal bounded control of the transient response of stochastic Rayleigh oscillator. First, the stochastic averaging method is adopted to obtain the partly averaged stochastic It?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 It?equation is obtained. The corresponding Fokker-Planck-Kolmogorov equation is obtained. Applying Galerkin procedure to the Fokker-Planck-Kolmogorov equation, an approximate solution is derived. The Monte-Carlo simulation is applied to the original system. The results obtained from the theory solutions and the digital solutions together show the accuracy and the effectiveness of the proposed procedure. |
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