First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

International Journal of Non-Linear Mechanics

Volumn 38, Issue 8, 2003, Pages 1133-1148

  Zhu, W Q ^a,b   Huang, Z L ^a   Deng, M L ^a  

^a ZHEJIANG UNIVERSITY   (China)

^b INSTITUTE OF MECHANICS   (China)

Author keywords

Dynamical programming; First passage failure; First passage time; Non linear system; Reliability; Stochastic averaging; Stochastic excitation; Stochastic optimal control

Indexed keywords

BOUNDARY CONDITIONS; DEGREES OF FREEDOM (MECHANICS); DYNAMIC PROGRAMMING; FEEDBACK; FEEDBACK CONTROL; HAMILTONIANS; RANDOM PROCESSES; RELIABILITY;

STOCHASTIC EXCITATION;

NONLINEAR SYSTEMS;

EID: 0037412193     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(02)00058-6     Document Type: Article

References (24)

1. Bharucha-Reid A.T. Elements of Markov Processes and their Applications. 1960;McGraw-Hill, New York.
2. Cox D.R., Miller H.D. The Theory of Stochastic Processes. 1965;Chapman and Hall, New York.
3. Ariaratnam S.T., Pi H.N. On the first-passage time for envelope crossing for a linear oscillator. Int. J. Control. 18:1973;89-96.
4. Lennox W.C., Fraser D.A. On the first passage distribution for the envelope of a non-stationary narrow-band stochastic process. J. Appl. Mech. ASME. 41:1974;793-797.
5. Ariaratnam S.T., Tam D.S.F. Random vibration and stability of a linear parametrically excited oscillator. Z. Angew. Math. Mech. 59:1979;79-84.
6. Spanos P.D., Solomos G.P. Barrier crossing due to transient excitation. J. Eng. Mech. Div. ASCE. 110:1984;20-36.
7. Roberts J.B. First passage probability for nonlinear oscillator. J. Eng. Mech. Div. ASCE. 102:1976;851-866.
8. Roberts J.B. First-passage time for oscillator with nonlinear restoring forces. J. Sound Vib. 56:1978;71-86.
9. Roberts J.B. Response of an oscillator with nonlinear damping and a softening spring to non-white random excitation. Prob. Eng. Mech. 1:1986;40-48.
10. Roberts J.B. First-passage time for randomly excited nonlinear oscillator. J. Sound Vib. 109:1986;33-50.
11. Spanos P.D. Survival probability of non-linear oscillators subjected to broad-band random disturbance. Int. J. Non-Linear Mech. 17:1982;303-317.
12. W.Q. Zhu, Y. Lei, First passage time for state transition of randomly excited systems, Proceedings of the 47th Session of International Statistical Institute, Vol. LIII, Book 3, 1989, pp. 517-531 (Invited Papers).
13. Cai G.Q., Lin Y.K. On statistics of first-passage failure. J. Appl. Mech. ASME. 61:1994;93-99.
14. Zhu W.Q., Yang Y.Q. Stochastic averaging of quasi-non-integrable-Hamiltonian systems. J. Appl. Mech. ASME. 64:1997;157-164.
15. Zhu W.Q., Huang Z.L., Yang Y.Q. Stochastic averaging of quasi-integrable Hamiltonian systems. J. Appl. Mech. ASME. 64:1997;975-984.
16. Gan C.B., Zhu W.Q. First-passage failure of quasi-non-integrable-Hamiltonian systems. Int. J. Non-Linear Mech. 36:2001;209-220.
17. W.Q. Zhu, M.L. Deng, Z.L. Huang, First-passage failure of quasi integrable Hamiltonian systems, J. Appl. Mech. ASME, 69 (2000), in press.
18. Zhu W.Q., Ying Z.G. Optimal nonlinear feedback control of quasi-Hamiltonian systems. Sci. China (Ser. A). 42:1999;1213-1219.
19. Zhu W.Q., Ying Z.G., Soong T.T. An optimal nonlinear feedback control strategy for randomly excited structural systems. Nonlinear Dyn. 24:2001;31-51.
20. Zhu W.Q., Huang Z.L., Deng M.L. Feedback minimization of first-passage failure of quasi non-integrable Hamiltonian systems. Int. J. Non-Linear Mech. 37:2002;1057-1071.
21. W.Q. Zhu, Z.L. Huang, M.L. Deng, Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems, Optional Control Applications and Methods, submitted for publication.
22. Zhu W.Q., Ying Z.G., Ni Y.Q., Ko J.M. Optimal nonlinear stochastic control of hysteretic systems. J. Eng. Mech. ASCE. 126:2000;1027-1032.
23. Zhu W.Q., Huang Z.L., Suzuki Y. Stochastic averaging and Lyapunov exponent of quasi partially integrable Hamiltonian system. Int. J. Non-Linear Mech. 37:2002;419-437.
24. Afanas'ev V.N., Kolmanovski V.B., Nosov V.R. Mathematical Theory of Control System Design. 1996;Kluwer Academic Publishers, Dordrecht.