Asymptotic optimization of nonlinear singularly perturbed systems with control constrained by a hypersphere

We consider a terminal control problem for a nonlinear singularly perturbed system with constraints imposed on the right endpoint of the trajectories. The values of the multidimensional controls are bounded in the Euclidean norm. We suggest an algorithm for an approximate (in the asymptotic sense) solution of this problem. The key advantage of the algorithm is the following: the original problem splits into two optimal control problems of lower dimension, one of which is linear.