Descriptor system approach to nonlinear singularly perturbed optimal control problem

This paper considers the infinite horizon nonlinear quadratic optimal control problem for a singularly perturbed system which is nonlinear in both, the slow and the fast variables. The relationship between this problem and the analogous one for a descriptor system is investigated. Parameter-independent controllers are constructed that solve the problem for the descriptor system and lead the full-order system to the near-optimal performance. Estimates on the closeness of the cost under near-optimal controllers to the optimal one are obtained.