| LTV度量反馈控制问题的最优控制器 |
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| 引用本文： | 宫婷,卢玉峰. LTV度量反馈控制问题的最优控制器[J]. 数学研究及应用, 2011, 31(3): 393-401. DOI: 10.3770/j.issn:1000-341X.2011.03.002 |
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| 作者姓名： | 宫婷 卢玉峰 |
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| 作者单位： | 大连理工大学数学科学学院，辽宁 大连 116024;大连理工大学数学科学学院，辽宁 大连 116024 |
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| 基金项目： | 国家自然科学基金(Grant No.10971020). |
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| 摘 要： | In this paper,we consider the measurement feedback control problem for discrete linear time-varying systems within the framework of nest algebra consisting of causal and bounded linear operators.Based on the inner-outer factorization of operators,we reduce the control problem to a distance from a certain operator to a special subspace of a nest algebra and show the existence of the optimal LTV controller in two different ways：one via the characteristic of the subspace in question directly,the other via the duality theory.The latter also gives a new formula for computing the optimal cost.
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| 关 键 词： | LTV systems nest algebra control optimal controller duality. |
| 收稿时间： | 2010-10-25 |
| 修稿时间： | 2011-04-22 |
On the Optimal Controller for LTV Measurement Feedback Control Problem |
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| Ting GONG and Yu Feng LU. On the Optimal Controller for LTV Measurement Feedback Control Problem[J]. Journal of Mathematical Research with Applications, 2011, 31(3): 393-401. DOI: 10.3770/j.issn:1000-341X.2011.03.002 |
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| Authors: | Ting GONG and Yu Feng LU |
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| Affiliation: | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | In this paper, we consider the measurement feedback control problem for discrete linear time-varying systems within the framework of nest algebra consisting of causal and bounded linear operators. Based on the inner-outer factorization of operators, we reduce the control problem to a distance from a certain operator to a special subspace of a nest algebra and show the existence of the optimal LTV controller in two different ways: one via the characteristic of the subspace in question directly, the other via the duality theory. The latter also gives a new formula for computing the optimal cost. |
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| Keywords: | LTV systems nest algebra control optimal controller duality. |
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