J. Comp. Math., 30 (2012), pp. 2-13. |
Step-Like Contrast Structure of Singularly Perturbed Optimal Control Problem Mingkang Ni ^{1}, Limeng Wu ^{1} 1 Department of Mathematics, East China Normal University, Shanghai 200241, ChinaReceived 2011-2-23 Accepted 2011-5-24 Available online 2012-1-09 doi:10.4208/jcm.1110-m11si07 Abstract 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. Key words: Singular perturbation, Optimal control problem, Contrast structure. AMS subject classifications: 34B15, 34E15. Email: xiaovikdo@163.com, neamou123@163.com |