Internal Layer Solution of Singularly Perturbed Optimal Control Problem with Integral Boundary Condition

摘要

In this paper, we investigate a class of singularly perturbed optimal control problem with integral boundary condition. By means of k + sigma exchange lemma, the existence of internal layer solution for the optimal control problem is proved. Meanwhile, the uniformly valid asymptotic solution is constructed by the boundary function method. Finally, an example is given for illustrating the main result.