| 一般时滞系统最优控制的逐步优化方法 |
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| 引用本文： | 张焕水,宋信敏,谢立华.一般时滞系统最优控制的逐步优化方法[J].山东大学学报(理学版),2011,46(10):45-56. |
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| 作者姓名： | 张焕水 宋信敏 谢立华 |
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| 作者单位： | 1. 山东大学控制科学与工程学院,山东济南,250016
2. 南洋理工大学电子与电气工程学院,新加坡,639798 |
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| 基金项目： | Supported by the Taishan Scholar Construction Engineering by Shandong Government; the National Natural Science Foundation for Distinguished Young Scholars of China(60825304); the Major State Basic Research Development Program of China(973 Program)(2009cb320600) |
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| 摘 要： | 上世纪60年代以来，借助于动态规划，无时滞系统的最优控制已经得到了很好的解决，然而，经典的动态规划没有像无时滞系统中逐步导出控制器一样，成功地应用于时滞系统。在本文中，针对一般时滞系统的最优控制问题，通过引入一对偶的倒向随机系统并应用内积理论，将提出一个逐步优化算法。借助于该方法，我们可以逐步对线性二次型（LQ）进行完全平方，进而得到控制器的解析解。有趣的是，时滞系统的控制器设计等价于对偶的倒向随机时滞系统不同信号的估计器设计。所提出的一般方法是行之有效的，因为借助于此方法，我们可以将时滞系统的最优控制从确定整个控制序列旋即变为逐一确定序列的元。可以相信所给出的逐步优化算法也可以用于解决其他相关的复杂控制问题，如控制问题解的充要条件等。
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| 关 键 词： | 时滞 最优控制 乘性噪声 完全平方 动态规划 |
Stage-by-Stage optimization approach to optimal control for general time-delay systems |
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| ZHANG Huan-shui,SONG Xin-min,XIE Li-hua.Stage-by-Stage optimization approach to optimal control for general time-delay systems[J].Journal of Shandong University,2011,46(10):45-56. |
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| Authors: | ZHANG Huan-shui SONG Xin-min XIE Li-hua |
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| Institution: | ZHANG Huan-shui1,SONG Xin-min1,XIE Li-hua2 (1.School of Control Science and Engineering,Shandong University,Jinan 250061,Shandong,China,2.School of Electrical and Electronic Engineering,Nanyang Technological University,Singapore 639798.) |
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| Abstract: | It is well known that the optimal control of delay-free systems has been well solved with dynamic programming since 60s of the last century,however the classical dynamic programming has not yet been successfully applied to time delay systems so as to derive the controller step by step as for delay-free systems.In this paper,we proposed a stage-by-stage optimization approach to the optimal control problem for general delayed systems by introducing an associated dual backward stochastic system and applying in... |
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| Keywords: | Time delay optimal control multiplicative noise completing the square dynamic programming |
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