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高校应用数学学报
高校应用数学学报  2019, Vol. 34 Issue (2): 203-    
    
时变四块问题的对偶理论方法
宫婷, 卢玉峰
1. 东北财经大学数学学院, 辽宁大连116025;
2. 大连理工大学数学科学学院, 辽宁大连116024
Duality theory for the time-varying 4-block problem
GONG Ting, LU Yu-feng
1. School of Mathematics, Dongbei University of Finance and Economics, Dalian 116025, China;
2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
 全文: PDF(337 KB)  
摘要： 利用算子理论方法研究最优控制中的重要问题{块问题的解法. 通过计算时
变四块问题中出现的子空间的零化子与预零化子, 建立起针对该问题的对偶理论, 从
而确保最优控制器的存在性并得到最优性能指标的计算公式. 经验证, 现有关于时变
一块与两块问题的对偶方法均可作为所得结论的特例. 此外, 举例说明当被控系统为
紧算子时, 由对偶理论提供的最优解具有时变全通性.
关键词： 块问题;  算子理论;  对偶理论;  线性时变系统;  最优控制    
Abstract: This paper solves the block problems which play a fundamental role in the optimal
control theory under the operator-theoretic framework. Speciˉc duality theory is established for 4-block
problem by computing the appropriate annihilator and preannihilator of subspaces in such optimal
problem. Existence of optimal controllers is ensured and formulas for the performance index are
derived. It is also shown that the known results about duality theories for time-varying 1-block and
2-block problems are both special cases of the presented results in this paper. Moreover, an example
is given to prove that the optimum obtained by duality theory for a compact plant is time-varying allpass.
Key words: block problems    operator theory    duality theory    linear time-varying system    optimal control
出版日期: 2019-07-05
CLC:  O177.2  
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引用本文:

宫婷, 卢玉峰. 时变四块问题的对偶理论方法[J]. 高校应用数学学报, 2019, 34(2): 203-.

GONG Ting, LU Yu-feng. Duality theory for the time-varying 4-block problem. Applied Mathematics A Journal of Chinese Universities, 2019, 34(2): 203-.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2019/V34/I2/203

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