%0 Journal Article
%T Conjugate Gradient-Boundary Element Method to Distributed Optimal Control Problem<br>分布参数最优控制的边界元共轭梯度算法
%A LI Bingjie
%A LIU Sanyang
%A <br>李炳杰
%A 刘三阳
%J 系统科学与数学
%D 2008
%I 
%X The numerical solution of distributed optimal control of a linear elliptic problem is investigated. The system of optimality consisting of state and costate variables (Lagrangian multiplier)for the optimal control is derived, and in convex condition, uniqueness of optimal solution is proved. The optimal control problem is translated into a kind of two players game problem which is a non-cooperative Stackelberg game between control function and state function. The Nash equilibrium point for the new system is the solution of the optimal control problem. The conjugate gradient-boundary element method for solving the Nash equilibrium point is developed. Finally, theerror estimates for these schemes are obtained. Numerical resultsindicate that the approach can save substantial computational work and that the algorithm is effective.
%K Distributed optimal control
%K fundamental solution
%K boundary element method
%K Nash equilibrium point
%K conjugate gradient method<br>分布参数最优控制
%K 基本解
%K 边界元方法
%K Nash平衡点.共轭梯度算法
%K 分布参数
%K 最优控制
%K 边界元
%K 共轭梯度算法
%K PROBLEM
%K OPTIMAL
%K CONTROL
%K DISTRIBUTED
%K METHOD
%K ELEMENT
%K 验证
%K 算例
%K 误差估计
%K 离散
%K 平衡点
%K 合作对策
%K Stackelberg
%K 局中人
%K 状态函数
%K 控制函数
%K 问题化
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=D708C1333F2222E5C7E42A8F3EC007D4&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=94C357A881DFC066&sid=65FC738C50B41E43&eid=70E3F4DEB0172F14&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=14