TY - JOUR

T1 - The Method of Averaged Models for Discrete-Time Adaptive Systems

AU - Amelina, N. O.

AU - Granichin, O. N.

AU - Fradkov, A. L.

N1 - Funding Information: This work was supported in part by the Russian Foundation for Basic Research, projects nos. 17-08-01728, 19-03-00375. The results on the analysis of continuous-discrete and networked systems in Sections 8-11 were obtained at the Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, under the support of the Russian Science Foundation, project no. 16-19-00057-P. Publisher Copyright: © 2019, Pleiades Publishing, Ltd.

PY - 2019/10/16

Y1 - 2019/10/16

N2 - 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.

AB - 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.

KW - dynamical systems

KW - nonlinear stochastic equations

KW - adaptive systems

KW - methods to simplify description

KW - approximate averaged models

KW - STOCHASTIC-APPROXIMATION

KW - WEAK-CONVERGENCE

KW - ALGORITHMS

KW - EIGENVALUES

KW - INFORMATION

KW - CONSENSUS

KW - FILTERS

KW - ERROR

UR - http://www.scopus.com/inward/record.url?scp=85073615476&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/method-averaged-models-discretetime-adaptive-systems

U2 - 10.1134/S0005117919100011

DO - 10.1134/S0005117919100011

M3 - статья

VL - 80

SP - 1755

EP - 1782

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 10

ER -