Exact design manifold control of nonlinear singularity perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behaviour of singularly perturbed systems. An important class of non-linear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.