一类含有叠层的线性奇摄动状态调节器问题  

A Class of Singularly Perturbed Linear State Regulator Problem with the Overlapping Layer

作　　者：葛志新[1] 陈咸奖[2] 

机构地区：[1]安徽工业大学数理学院,马鞍山243002 [2]安徽工业大学商学院,马鞍山243002

出　　处：《应用数学学报》2015年第6期1050-1058,共9页Acta Mathematicae Applicatae Sinica

基　　金：安徽省高校优秀青年人才基金项目(2012SQRL037)

摘　　要：本文研究了一类含有叠层的奇摄动线性状态调节器问题.首先引进三个共态量和一个哈密尔顿函数,寻找出最优控制条件的充要条件,然后在一定的条件下,先分别构造原函数和共态量的合成解形式,再利用原问题的退化形式和不同的伸长变量,依据校正项特有的性质,分别计算出原函数和共态量表达式,得到最优控制的表达式,从而获得状态调节器性能指标的渐近形式,发现边界层校正项对最优性能指标影响在高阶上.A class of singularly perturbed linear state regulator problem with the overlapping layer is studied in this paper. First, three costate variable and Hamiltonian are introduced. A sufficient and necessary condition is obtained for the optimal control. Then, under certain conditions, the forms of component solutions of the original functions and the three costate variables are structured. Based on the degenerate case of the original problem, the various stretched variables and the nature of the correction terms, the expressions of the original functions and the costate variables are given respectively. The expression of the optimal control is obtained. The asymptotic solution of linear state regulator problem is obtained. So, we obtain the asymptotic expansion of the optimal cost. We find the optimal cost is influenced on its higher-order terms by the correction terms of the original functions and the three costate variables.

关 键 词：奇摄动 状态调节器 叠层 

分 类 号：O175.14[理学—数学]