On the convergence of gradient projection methods for non-convex optimal control problems with affine system

. This paper is devoted to study the convergence theory of Gradient Projection Method (briefly GPM) for nonconvex optimal control problems with affine system. We show that if the cost functional is quasi-convex, the iterative sequence of controls of GPM converge strongly to the optimal control. Moreover, under some mild assumptions, we also obtain the linear convergence rate of GPM. Finally, the theoretical results have been demonstrated by some numerical experiments.