Step-like contrast structure for class of nonlinear singularly perturbed optimal control problem  

作　　者：武利猛 倪明康 陆海波 

机构地区：[1]School of Mathematics and Information Technology, Hebei Normal University of Science and Technology [2]Department of Mathematics, East China Normal University [3]Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Jiao Tong Univeristy

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第7期875-888,共14页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 11071075 and 11171113);the E-Institute of Shanghai Municipal Education Commission (No. E03004);the Knowledge Innovation Program of the Chinese Academy of Sciences (Nos. 30921064 and 90820307)

摘　　要：The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control problem is proved by equivalence, which is based on the necessary conditions. The authors not only give the conditions under which there exists a step-like contrast structure, but also determine where the internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of the step-like contrast structure solution is constructed by the direct scheme method. Finally, an example is presented to show the result.The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control problem is proved by equivalence, which is based on the necessary conditions. The authors not only give the conditions under which there exists a step-like contrast structure, but also determine where the internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of the step-like contrast structure solution is constructed by the direct scheme method. Finally, an example is presented to show the result.

关 键 词：optimal control contrast structure singular perturbation 

分 类 号：O232[理学—运筹学与控制论]