The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit...The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.展开更多
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 pro...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.展开更多
The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct ...The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. As an application, an example is given to illustrate the main result in this paper.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11071075)the Natural Science Foundation of Shanghai(No.10ZR1409200)
文摘The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.
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)
文摘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.
基金Acknowledgments. The authors are grateful to Professor Zhiming Wang of East China Normal University for his comments which improved the presentation of the paper. The research was supported by the National Natural Science Foundation of China （11071075, 30921064, 90820307）, Natural Science Foundation of Shanghai （10ZR1409200）, E-Institutes of Shanghai Municipal Education Commission （E03004）, the Knowledge Innovation Program of the Chinese Academy of Sciences.
文摘The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. As an application, an example is given to illustrate the main result in this paper.
