A new reduction technique for a class of singularly perturbed optimal control problems

We consider a class of singularly perturbed optimal control problems which may not be approximated by the reduced problems constructed via the formal replacement of the fast variables by the states of equilibrium of the “fast” subsystem considered with “frozen” slow variables and controls. We construct a reduced optimal control problem which provides a true approximation for the problems under consideration and write down the necessary and sufficient optimality conditions for this reduced problem