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Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.9 P.1245~1251

http://doi.org/10.1631/jzus.A0820316


Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations


Author(s):  Lin-cong CHEN, Rong-hua HUAN, Wei-qiu ZHU

Affiliation(s):  Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   wqzhu@yahoo.com

Key Words:  Stochastic optimal control, Dynamical programming, Quasi integrable-Hamiltonian system, Stochastic averaging, Combined harmonic and white noise excitation, Reliability


Lin-cong CHEN, Rong-hua HUAN, Wei-qiu ZHU. Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations[J]. Journal of Zhejiang University Science A, 2009, 10(9): 1245~1251.

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author="Lin-cong CHEN, Rong-hua HUAN, Wei-qiu ZHU",
journal="Journal of Zhejiang University Science A",
volume="10",
number="9",
pages="1245~1251",
year="2009",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A0820316"
}

%0 Journal Article
%T Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations
%A Lin-cong CHEN
%A Rong-hua HUAN
%A Wei-qiu ZHU
%J Journal of Zhejiang University SCIENCE A
%V 10
%N 9
%P 1245~1251
%@ 1673-565X
%D 2009
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820316

TY - JOUR
T1 - Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations
A1 - Lin-cong CHEN
A1 - Rong-hua HUAN
A1 - Wei-qiu ZHU
J0 - Journal of Zhejiang University Science A
VL - 10
IS - 9
SP - 1245
EP - 1251
%@ 1673-565X
Y1 - 2009
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820316


Abstract: 
We studied the feedback maximization of reliability of multi-degree-of-freedom (MDOF) quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Itô equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Chen, L.C., Zhu, W.Q., 2008. First passage failure of quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Acta Mechanica, 206(3-4):133-148.

[2] Huang, Z.L., Zhu, W.Q., 2004. Stochastic averaging of quasi integrable Hamiltonian systems under combined harmonic and white noise excitations. International Journal of Non-Linear Mechanics, 39:1413-1421.

[3] Luo, M., Zhu, W.Q., 2006. Nonlinear stochastic optimal control of offshore platforms under wave loading. Journal of Sound and Vibration, 296(4-5):734-745.

[4] Ying, Z.G., Ni, Y.Q., Ko, J.M., 2007. A bounded stochastic optimal semi-active control. Journal of Sound and Vibration, 304(3-5):948-956.

[5] Zhu, W.Q., 2004. Feedback stabilization of quasi nonintegrable Hamiltonian systems by using Lyapunov exponent. Nonlinear Dynamics, 36(2-4):455-470.

[6] Zhu, W.Q., Ying, Z.G, 1999. A nonlinear feedback control of quasi Hamiltonian systems. Science in China Series A: Mathematics, 42(11):1213-1219.

[7] Zhu, W.Q., Deng, M.L., 2007. Feedback minimization of first-passage failure of quasi integrable-Hamiltonian systems. Acta Mechanica Sinica, 23(4):437-444.

[8] Zhu, W.Q., Ying, Z.G, 2004. On stochastic optimal control of partially observable nonlinear quasi-Hamiltonian systems. Zhejiang University SCIENCE, 5(11):1313-1317.

[9] Zhu, W.Q., Ying, Z.G, Soong, T.T., 2001. An nonlinear feedback control strategy for randomly excited structural systems. Nonlinear Dynamics, 24(1):31-51.

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