| 无穷维最优控制系统的N阶近似 |
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| 引用本文： | 郑应文.无穷维最优控制系统的N阶近似[J].福州大学学报(自然科学版),1996(1):34-38. |
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| 作者姓名： | 郑应文 |
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| 作者单位： | 福州大学自动化研究所 |
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| 基金项目： | 中国科学院复杂系统控制开放实验室 |
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| 摘 要： | 讨论一类用无穷维系统方程描述的最优控制问题，把它看作为Ｈｉｌｂｅｒｔ空间上求算子方程的最小均方解的问题．在无穷维算子近似理论的基础上，用无穷矩阵奇异值分解方法得到无穷维最优控制问题解的形式，并研究这个解的有限维近似形式，建立一个有限的Ｎ阶最优控制系统，使得它的控制律与无穷维系统的控制之间误差最小
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| 关 键 词： | 无穷维系统 最优控制 近似 奇异值 |
N Approximation to the Infinite Dimension Optimal Control Systems |
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| Zheng Yingwen.N Approximation to the Infinite Dimension Optimal Control Systems[J].Journal of Fuzhou University(Natural Science Edition),1996(1):34-38. |
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| Authors: | Zheng Yingwen |
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| Institution: | Zheng Yingwen (Institute of Automation,Fuzhou University,Fuzhou,350002) |
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| Abstract: | The optimal control problem described by the infinite dimensional system equations is discussed.It is regarded as a least squares solution of the operator equations in Hilbert space.Based on the infinite dimensional operator approximate theory,an optimal solution and its finite dimensional approximatc solution of the infinite dimensional systems are provided by means of the infinite matrix SVD method.An N dimension optimal control system is reconstructed to approximate the infinite dimensional system in which the norm error between their control laws is mininal. |
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| Keywords: | infinite dimensional systems optimal control approximation singular values |
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