The Method of Averaged Models for Discrete-Time Adaptive Systems

Dynamical processes in nature and technology are usually described by continuous-or discrete-time dynamical models, which have the form of nonlinear stochastic differential or difference equations. Hence, a topical problem is to develop effective methods for a simpler description of dynamical systems. The main requirement to simplification methods is preserving certain properties of a process under study. One group of such methods is represented by the methods of continuous- or discrete-time averagedmodels, which are surveyed in this paper. New results for stochastic networked systems are also introduced. As is shown below, the method of averaged models can be used to reduce the analytical complexity of a closed loop stochastic system. The corresponding upper bounds on the mean square distance between the states of an original stochastic system and its approximate averaged model are obtained.