Mean square stabilisation of complex oscillatory regimes in nonlinear stochastic systems / Bashkirtseva Irina,Ryashko Lev // INTERNATIONAL JOURNAL OF CONTROL. - 2016. - V. 89, l. 4. - P. 793-800.

ISSN/EISSN:

0020-7179 / 1366-5820

Type:

Article

Abstract:

A problem of stabilisation of the randomly forced periodic and quasiperiodic modes for nonlinear dynamic systems is considered. For this problem solution, we propose a new theoretical approach to consider these modes as invariant manifolds of the stochastic differential equations with control. The aim of the control is to provide the exponential mean square (EMS) stability for these manifolds. A general method of the stabilisation based on the algebraic criterion of the EMS-stability is elaborated. A constructive technique for the design of the feedback regulators stabilising various types of oscillatory regimes is proposed. A detailed parametric analysis of the problem of the stabilisation for stochastically forced periodic and quasiperiodic modes is given. An illustrative example of stochastic Hopf system is included to demonstrate the effectiveness of the proposed technique.

Author keywords:

invariant manifolds; feedback; oscillatory regimes; cycles, tori; Stabilisation INVARIANT-MANIFOLDS; STABILITY; DELAY

DOI:

10.1080/00207179.2015.1099739

Web of Science ID:

ISI:000370544500012

Соавторы в МНС:

Другие поля

Поле	Значение
Month	APR 2
Publisher	TAYLOR \& FRANCIS LTD
Address	2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Language	English
EISSN	1366-5820
Keywords-Plus	INVARIANT-MANIFOLDS; STABILITY; DELAY
Research-Areas	Automation \& Control Systems
Web-of-Science-Categories	Automation \& Control Systems
Author-Email	irina.bashkirtseva@urfu.ru
Funding-Acknowledgement	RFBR {[}13-08-00069]; Government of the Russian Federation (Act 211) {[}02.A03.21.0006]
Funding-Text	This work was partially supported by RFBR (13-08-00069) and by the Government of the Russian Federation (Act 211, contract 02.A03.21.0006).
Number-of-Cited-References	29
Usage-Count-Since-2013	2
Journal-ISO	Int. J. Control
Doc-Delivery-Number	DE3QJ