基于边界元的分布参数最优控制共轭梯度算法  

Conjugate gradient algorithm based on boundary element method to distributed elliptic optimal control problem

作　　者：李炳杰[1,2] 刘三阳[1] 

机构地区：[1]西安电子科技大学理学院数学系 [2]空军工程大学理学院,陕西西安710038

出　　处：《兰州大学学报（自然科学版）》2006年第4期140-144,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：陕西省自然科学基金资助项目(2004 A05).

摘　　要：得到椭圆型分布参数最优控制问题对应的最优性方程组,在凸性条件下,证明了最优控制的唯一存在性问题．利用一阶最优性条件构造了基于边界元法的共轭梯度算法,给出算法的局部误差估计．最后,以算例验证算法的有效性．A system of optimality equations of distributed elliptic optimal control problem is derived and, in the convex condition, the existence of a unique solution to optimal control problem is proved. The conjugate gradient algorithm based on boundary element method is developed by means of the associated first-order necessary optimality condition and the local error estimates for this scheme is obtained. Finally, a numerical example is given to illustrate the efficiency of the proposed methodology.

关 键 词：最优控制 基本解 边界元方法 共轭梯度算法 

分 类 号：O241.8[理学—计算数学] O231.4[理学—数学]