STEP-LIKE CONTRAST STRUCTURE OF SINGULARLY PERTURBED OPTIMAL CONTROL PROBLEM＊

In this paper, the existence of step-like contrast structure for a class of singularly perturbed optimal control problem is shown by the 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. Finally, an example is presented to show the result. 2000 Mathematics Subject Classification. 34B15; 34E15.