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Avtomat. i Telemekh., 2019, Issue 10, Pages 3–36 (Mi at15363)  

The method of averaged models for discrete-time adaptive systems

N. O. Amelinaab, O. N. Granichinba, A. L. Fradkovab

a St. Petersburg State University, St. Petersburg, Russia
b Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: 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.

Keywords: dynamical systems, nonlinear stochastic equations, adaptive systems, methods to simplify description, approximate averaged models.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-08-01728_
19-03-00375
Russian Science Foundation 16-19-00057-
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 811 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.


DOI: https://doi.org/10.1134/S0005231019100015

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English version:
Automation and Remote Control, 2019, 80:10, 1755–1782

Bibliographic databases:


Received: 19.07.2018
Revised: 06.09.2018
Accepted: 08.11.2018

Citation: N. O. Amelina, O. N. Granichin, A. L. Fradkov, “The method of averaged models for discrete-time adaptive systems”, Avtomat. i Telemekh., 2019, no. 10, 3–36; Autom. Remote Control, 80:10 (2019), 1755–1782

Citation in format AMSBIB
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