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

Abstract We study the infinite horizon nonlinear quadratic optimal control problem for a singularly perturbed system, which is nonlinear in both, the slow and the fast variables. It is known that the optimal controller for such problem can be designed by finding a special invariant manifold of the corresponding Hamiltonian system. We obtain exact slow–fast decomposition of the Hamiltonian system and of the special invariant manifold into the slow and the fast ones. On the basis of this decomposition we construct high-order asymptotic approximations of the optimal state-feedback and optimal trajectory.

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