Regularization of cheap periodic control problems

A regularization method for cheap periodic control problems is designed. The periodic problem for singularly perturbed Riccati matrix differential equations is reduced to an extended system of singularly perturbed initial problems. This system admits the application of a geometric approach based on the use of integral manifolds and, consequently, dimensional reduction. The solution is asymptotically expanded in fractional powers of a small parameter. An example on control of periodic oscillations of a mechanical system is given.