平稳河道水波模型的最优控制  

Optimal Control of Stationary River Wave Model

作　　者：乔正明[1] 冯志刚[2] 王成杰[1] 

机构地区：[1]常州纺织服装职业技术学院基础部,江苏常州213164 [2]江苏大学理学院,江苏镇江212013

出　　处：《河海大学常州分校学报》2007年第3期18-21,共4页Journal of Hohai University Changzhou

摘　　要：研究平稳静态河道水波模型的最优控制问题.应用分布式参数系统最优控制理论和相关的泛函Sobolve空间知识,选择轨迹型的性能指标和特殊的Banach空间,证明平稳模型方程在Dirichlet边界条件下最优解的存在性.通过引入Lagrangian乘子将等式约束和轨迹型性能指标转化为Lagrangian项和罚函数项,并用非线性泛函中的Frechet导数和变分不等式研究了最优解存在的一阶必要和二阶充分最优条件.此条件是研究浅水波模型最优控制可计算性理论和实际应用的基础.The optimal control problems for the stationary river wave model are analyzed. Using distributed parameter system optimal control theory and related functional analysis of Sobolve space, and selecting cost functional of tracking type, special Banach space, it is proved that the optimal solution of stationary model equation exists under Dirichlet boundary condition. In addition, a Lagrange multiplier is introduced so that the equality constraint and cost functional is realized by a Lagrangian term together with a penalty functional, and the first and second order necessary considered by using the Frechet-derivative of nonlinear and sufficient conditions for optimal solution are functional analysis and variational inequality. The resuhs may contribute to the further research on computational optimal control theory of shallow wave model and practical application.

关 键 词：河道水波模型 RLW-BURGERS方程 最优控制 一阶必要条件 二阶充分条件 

分 类 号：O241.82[理学—计算数学]