Stabilization of stochastic cycles and chaos suppression for nonlinear discrete-time systems / Bashkirtseva I.,Ryashko L. // NONLINEAR DYNAMICS. - 2012. - V. 67, l. 4. - P. 2505-2517.

ISSN/EISSN:

0924-090X / 1573-269X

Type:

Article

Abstract:

In this paper we consider a nonlinear discrete-time control system with regular and chaotic dynamics forced by stochastic disturbances. The problem addressed is the design of the feedback regulator which stabilizes a limit cycle of the closed-loop deterministic system and synthesizes a required dispersion of random states for the corresponding stochastic system. To solve this problem, we propose a new method based on the stochastic sensitivity function technique. This function approximates a dispersion of random states distributed around deterministic cycle. Explicit formulas for the intercoupling between stochastic sensitivity function and considered system parameters are worked out. The problem of the design of the required stochastic sensitivity function for cycles by feedback regulators is solved. Coefficients of the feedback regulator are constructed and corresponding attainability sets are described. The effectiveness of the proposed approach is demonstrated on the stochastic Verhulst model. It is shown that constructed regulators provide a low level of sensitivity and suppress chaotic oscillations.

Author keywords:

Stochastic disturbances; Chaos control; Stochastic sensitivity; Stabilization of cycles NOISE; SENSITIVITY; OSCILLATIONS; 3D-CYCLES; ORDER

DOI:

10.1007/s11071-011-0163-7

Web of Science ID:

ISI:000300187500015

Соавторы в МНС:

Другие поля

Поле	Значение
Month	MAR
Publisher	SPRINGER
Address	VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
Language	English
EISSN	1573-269X
Keywords-Plus	NOISE; SENSITIVITY; OSCILLATIONS; 3D-CYCLES; ORDER
Research-Areas	Engineering; Mechanics
Web-of-Science-Categories	Engineering, Mechanical; Mechanics
Author-Email	lev.ryashko@usu.ru
Funding-Acknowledgement	Federal Education Agency {[}2.1.1/2571]; Federal Target Program {[}N 02.740.11.0202]; {[}RFBR09-01-00026]; {[}09-08-00048]; {[}10-01-96022\_ural]
Funding-Text	This work was partially supported by grants RFBR09-01-00026, 09-08-00048, 10-01-96022\_ural, Federal Education Agency 2.1.1/2571, Federal Target Program N 02.740.11.0202.
Number-of-Cited-References	40
Usage-Count-Since-2013	6
Journal-ISO	Nonlinear Dyn.
Doc-Delivery-Number	891AC