Exact slow-fast decomposition of the nonlinear singularly perturbed optimal control problem

We study the infinite horizon nonlinear quadratic optimal control problem f or a singularly perturbed system, which is nonlinear in both, the slow and the fast variables. It is known that the optimal controller for such proble m can be designed by finding a special invariant manifold of the correspond ing Hamiltonian system. We obtain exact slow-fast decomposition of the Hami ltonian system and of the special invariant manifold into the slow and the fast ones. On the basis of this decomposition we construct high-order asymp totic approximations of the optimal state-feedback and optimal trajectory. (C) 2000 Elsevier Science B.V. All rights reserved.