Burgers方程初边值条件的控制

ON THE INITIAL BOUNDARY CONDITION CONTROL FOR BURGERS EQUATION

为将优化控制技巧用于复杂的地球物理环流模型及其它领域 ,以Burgers方程为模型 ,描述了初边值条件的优化控制 .在一般化的意义上 ,给出了连续问题及其相应的离散形式 .引入伴随变量 ,并由此导出伴随方程 .比较初始控制中不同频率误差对优化控制的影响 ,分析了用有限观测数据作空间插值后的数据、方法的优化控制能力及效果 。

In order to use the optimal control techniques in the models of geophysical flow circulation and other research fields, an application with the control of initial and boundary conditions to Brugers equation is described. In a general case, the continuous problem and corresponding discrete form are formulated, in which the so called adjoint variable is introduced and then the adjoint equation is derived. The impacts on the optimal control for the error with various frequencies in initial control are considered. The effects and ability of this optimal control method are analyzed, in which the observational data used are obtained by the linear interpolating in spatial grids from original observational data. This method proves to be efficient and useful.