| 引用本文: | 朱其吉.一类半线性椭圆型分布参数控制系统的最大值原理[J].控制理论与应用,1986,3(3):120~129.[点击复制] |
| Zhu Qiji.MAXIMUM PRINCIPLE FOR CONTROL SYSTEM GOVERNED BY ELLIPTIC PARTIAL DIFFERENTIAL EQUATION[J].Control Theory and Technology,1986,3(3):120~129.[点击复制] |
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| 一类半线性椭圆型分布参数控制系统的最大值原理 |
| MAXIMUM PRINCIPLE FOR CONTROL SYSTEM GOVERNED BY ELLIPTIC PARTIAL DIFFERENTIAL EQUATION |
| 摘要点击 833 全文点击 488 投稿时间：1983-12-24 修订日期：1986-03-17 |
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| DOI编号 |
| 1986,3(3):120-129 |
| 中文关键词 |
| 英文关键词 |
| 基金项目 |
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| 中文摘要 |
| 本文给出半线性椭圆型分布参数控制系统
Ay(u)+b(u,y(u))=f(u),
Y(u)Ⅰ??=0,
在一般泛函指标下的最大值原理。 |
| 英文摘要 |
| In this paper, we consider the following optimal control problem:
minimize∫?g(y(u),u)
subject to
Ay(u)+b(u,y(u))=f(u)
where A is a elliptic partial differential operator of second order and b, f, g are functions satisfying certain smooth conditions. The main result is:
Theorem. Let u*∈Uod be the solution of the above problem and y* be the corresponding solution of the control system. Then for almost all x∈?, we have
p*(x)(b(x,u*(x),y*(x))-f(x,u*(x)))-g(x,y*(x),u*(x))
=max p*(x)(b(x,u*(x),y*(x))-f(x,u)-g(x,y*(x),u)
where p*( 。) is the solution of the corresponding adjoint system
Ap*+?b/?y(u*,y*), p*Ι??=0
Example of applications is given. |
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