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Title: Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information

Abstract

A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.

Authors:
 [1]
  1. Ural Federal University, Lenina, 51, Ekaterinburg, 620000 (Russian Federation)
Publication Date:
OSTI Identifier:
22494298
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1690; Journal Issue: 1; Conference: AMEE '15: 41. international conference on applications of mathematics in engineering and economics, Sozopol (Bulgaria), 8-13 Jun 2015; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; AMPLITUDES; EQUATIONS; EQUILIBRIUM; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STABILIZATION; STOCHASTIC PROCESSES

Citation Formats

Ryashko, Lev. Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information. United States: N. p., 2015. Web. doi:10.1063/1.4936692.
Ryashko, Lev. Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information. United States. doi:10.1063/1.4936692.
Ryashko, Lev. Mon . "Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information". United States. doi:10.1063/1.4936692.
@article{osti_22494298,
title = {Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information},
author = {Ryashko, Lev},
abstractNote = {A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.},
doi = {10.1063/1.4936692},
journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1690,
place = {United States},
year = {2015},
month = {11}
}