Optimal Bounded Control of First-Passage Failure of Quasi-Integrable Hamiltonian Systems with Wide-Band Random Excitation

Nonlinear Dynamics

Volumn 33, Issue 2, 2003, Pages 189-207

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

^a ZHEJIANG UNIVERSITY   (China)

^b INSTITUTE OF MECHANICS   (China)

Author keywords

First passage time; Nonlinear system; Random excitation; Stochastic optimal control

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HAMILTONIANS; OPTIMAL CONTROL SYSTEMS;

STOCHASTIC OPTIMAL CONTROL;

NONLINEAR SYSTEMS;

EID: 0142153900     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026049216559     Document Type: Article

References (33)

1. Bharucha-Reid, A. T., Elements of Markov Processes and Their Applications, McGraw-Hill, New York, 1960.
2. Cox, D. R. and Miller, H. D., The Theory of Stochastic Processes, Chapman and Hall, New York, 1965.
3. Ariaratnam, S. T. and Pi, H. N., 'On the first-passage time for envelope crossing for a linear oscillator', International Journal of Control 18, 1973, 89-96.
4. Lennox, W. C. and Fraser, D. A., 'On the first passage distribution for the envelope of non-stationary narrow-band stochastic process', ASME Journal of Applied Mechanics 41, 1974, 793- 797.
5. Ariaratnam, S. T. and Tam, D. S. F., 'Random vibration and stability of a linear parametrically excited oscillator', Zeitschrift für angewandte Mathematik und Mechanik 59, 1979, 79-84.
6. Spanos, P. D. and Solomos, G. P., 'Barrier crossing due to transient excitation', ASCE Journal of Engineering Mechanics Division 110,1984, 20-36.
7. Roberts, J. B., 'First passage probability for nonlinear oscillator', ASCE Journal of Engineering Mechanics Division 102, 1976, 851-866.
8. Roberts, J. B., 'First passage probability for oscillator with nonlinear restoring forces', Journal of Sound and Vibration 56, 1978, 71-86.
9. Roberts, J. B., 'Response of an oscillator with nonlinear damping and a softening spring to non-white random excitation', Probabilistic Engineering Mechanics 1, 1986, 40-48.
10. Roberts, J. B., 'First passage time for randomly excited nonlinear oscillator', Journal of Sound and Vibration 109, 1986, 33-50.
11. Spanos, P. D., 'Survival probability of non-linear oscillators subjected to broad-band random disturbance', International Journal of Non-Linear Mechanics 17, 1982, 303-317.
12. Zhu, W. Q. and Lei, Y., First passage time for state transition of randomly excited systems', in Proceedings of the 47th Session of International Statistical Institute, Vol. LIII (Invited Papers), Book 3, 1989, pp. 517-531.
13. Cai, G. Q. and Lin, Y. K., 'On statistics of first-passage failure', ASME Journal of Applied Mechanics 61, 1994, 93-99.
14. Zhu, W. Q. and Yang, Y. Q., 'Stochastic averaging of quasi-non- integrable-Hamiltonian systems', ASME Journal of Applied Mechanics 64, 1997, 157-164.
15. Zhu, W. Q., Huang, Z. L., and Yang Y. Q., 'Stochastic averaging of quasi- integrable Hamiltonian systems', ASME Journal of Applied Mechanics, 64, 1997, 975-984.
16. Zhu, W. Q., Huang, Z. L., and Suzuki, Y., 'Stochastic averaging and Lyapunov exponent of quasi-partially integrable Hamiltonian systems', International Journal of Non-Linear Mechanics 37, 2002, 419-437.
17. Gan, C. B. and Zhu, W. Q., 'First-passage failure of quasi-non-integrable- Hamiltonian systems', International Journal of Non-Linear Mechanics 36, 2001, 209-220.
18. Zhu, W. Q., Deng, M. L., and Huang, Z. L., 'First-passage failure of quasi- integrable Hamiltonian system', ASME Journal of Applied Mechanics 69, 2002, 274-282.
19. Zhu, W. Q., Huang, Z. L., and Deng, M. L., 'First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems', International Journal of Non- Linear Mechanics 38, 2003, 1133-1148.
20. Fleming, W. H. and Rishel, R. W., Deterministic and Stochastic Optimal Control, Springer, New York, 1975.
21. Fleming, W. H. and Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Springer, New York, 1992.
22. Yong, J. M. and Zhou, X. Y., Stochastic Controls, Hamiltonian Systems and HJB Equations, Springer, New York, 1999.
23. Bensoussan, A., Stochastic Control of Partially Observable Systems, Cambridge University Press, Cambridge, 1992.
24. Zhu, W. Q. and Ying, Z. G., 'Optimal nonlinear feedback control of quasi- Hamiltonian systems', Science in China, Series A 42, 1999, 1213-1219.
25. Zhu, W. Q., Ying, Z. G., and Soong, T. T., 'An optimal nonlinear feedback control strategy for randomly excited structural systems', Nonlinear Dynamics 24, 2001, 31-51.
26. Zhu, W. Q. and Ying, Z. G., 'Nonlinear stochastic optimally control of partially observable linear structures', Engineering Structures 24, 2002, 333-342.
27. Zhu, W. Q., Huang, Z. L., and Deng, M. L., 'Feedback minimization of first-passage failure of quasi-non-integrable Hamiltonian systems', International Journal of Non-Linear Mechanics 37, 2002, 1057-1071.
28. Zhu, W. Q. and Huang, Z. L., 'Feedback stabilization of quasi integrable Hamiltonian systems', ASME Journal of Applied Mechanics 70, 2003, 129-136.
29. Xu, Z. and Chung, Y. K., 'Averaging method using generalized harmonic functions for strongly nonlinear oscillators', Journal of Sound and Vibration 174, 1994, 563-576.
30. Stratonovich, R. L., Topics in the Theory of Random Noise, Vol. I, Gorden and Breach, New York, 1963.
31. Khasminskii, R. Z., 'A limit theorem for the solutions of differential equations with random right-hand sides', Theory of Probability and Applications 11, 1966, 390-406.
32. Papanicolaou, G. C. and Kohler, W., 'Asymptotic theory of mixing stochastic ordinary differential equations', Communications on Pure and Applied Mathematics 27, 1974, 641-668.
33. Kushner, H. J. and Runggaldier W., 'Nearly optimal state feedback controls for stochastic systems with wideband noise disturbances', SIAM Journal of Control and Optimization 25, 1987, 298-315.