Rapidly oscillating systems: averaging and control

A new class of perturbed systems, called rapidly oscillating systems, is presented in this paper. These systems have some interesting connections with classical averaging problems for perturbed systems, giving an averaging in several cases, where the classical theory does not work. Applications of rapidly oscillating systems include such areas as control of walking machines, simulation of biological and artificial neurons, rapid thermal processing of semiconductors, etc. Some specific control problems in these areas have been formulated and solved using this new averaging technique