| 引用本文: | 李佼瑞, 徐伟.随机Rayleigh振子的首次穿越和最优控制[J].控制理论与应用,2007,24(6):954~958.[点击复制] |
| LI Jiao-rui, XUWei.First-passage failure and optimal control of stochastic Rayleigh oscillator[J].Control Theory and Technology,2007,24(6):954~958.[点击复制] |
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| 随机Rayleigh振子的首次穿越和最优控制 |
| First-passage failure and optimal control of stochastic Rayleigh oscillator |
| 摘要点击 1561 全文点击 1303 投稿时间：2005-07-14 修订日期：2006-12-27 |
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| DOI编号 10.7641/j.issn.1000-8152.2007.6.017 |
| 2007,24(6):954-958 |
| 中文关键词 Rayleigh 振子 随机平均法 首次穿越 随机稳定化 |
| 英文关键词 Rayleigh oscillator stochastic averaging method first-passage failure stochastic stabilization |
| 基金项目 国家自然科学基金资助项目(10472091); 国家自然科学基金重点资助项目(10333020) |
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| 中文摘要 |
| 研究随机Rayleigh振子的首次穿越和最优控制问题. 利用随机平均法给出了系统运动方程的随机平均微分方程, 并对平均方程建立了条件可靠性函数的后向Kolmogorov方程, 得出相应的首次穿越条件概率密度函数, 并利用Lyapunov指数法对受控系统的平均方程进行了随机稳定化, 得到了最优控制率. |
| 英文摘要 |
| The first-passage failure and optimal control of stochastic Rayleigh oscillator are studied in this paper. An averaged It^o stochastic differential Equation of the stochastic system is reduced by using the stochastic averaging method. A backward Kolmogorov Equation governing the conditional reliability function of first passage failure is then established.The conditional reliability function and the conditional probability density are also obtained by solving the backward Kolmogorov Equation with boundary conditions. Finally, an optimal control law of this system is obtained. |