具有Neumann边值条件时滞抛物系统的最优边界控制  

Optimal boundary control of retarded parabolic systems with Neumann boundary condition

作　　者：李宏飞[1] 罗学波[1] 

机构地区：[1]西北工业大学数学与信息科学系,陕西西安710072

出　　处：《西北大学学报（自然科学版）》2004年第2期128-132,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家"973"重点基础研究发展计划基金资助项目(G1998030417)

摘　　要：目的　为获得Neumann边值条件下最优性条件,讨论了一类具有时滞的分布抛物型系统的最优边界控制问题。方法　通过性能泛函的Fr啨chet导数和控制约束区域的凸性给出最优问题的一个等价条件,进而引入系统的伴随方程简化此条件。结果　得到了系统在Neumann边值条件下最优解存在的充分必要条件。结论　对于所研究的抛物系统的两类性能指标,由变分不等式分别给出了最优控制存在的最大值条件,对文献的相关结果有所发展。AimThe optimal boundary control problems for distributed parabolic systems in which retarded arguments appear in the integral form in the state equations are discussed.The optimal conditions are given.MethodsThe equivalent condition of the optimal problem is presented by Fréchet derivative of the performance functional and the convex property of constrained control region, which is further simplified by introducing the adjoint equation.ResultsNecessary and sufficient conditions of optimality for the third boundary value problem with the quadratic performance functional and constrained control are derived.ConclusionTo two different performances functional of the system,the maximum conditions for the existence of optimal control are respectively presented by variational inequalities, which expand those known results.

关 键 词：时滞抛物系统 边界控制 最优控制 Neumann边值条件 

分 类 号：O175.27[理学—数学]