Optimal Bounded Control for Minimizing the Response of Quasi Non-integrable Hamiltonian Systems

Nonlinear Dynamics

Volumn 35, Issue 1, 2004, Pages 81-100

  Zhu, W Q ^a   Deng, M L ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Dynamical programming; Nonlinear system; Stochastic averaging; Stochastic excitation; Stochastic optimal control

Indexed keywords

DAMPING; DIFFERENTIAL EQUATIONS; DYNAMIC PROGRAMMING; HAMILTONIANS; OPTIMAL CONTROL SYSTEMS; RANDOM PROCESSES;

STOCHASTIC EXCITATION; STOCHASTIC OPTIMAL CONTROL;

NONLINEAR SYSTEMS;

EID: 1642588274     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NODY.0000017495.70390.b3     Document Type: Article

References (21)

1. Fleming, W. H. and Rishel, R. W., Deterministic and Stochastic Optimal Control, Springer, New York, 1975.
2. Fleming, W. H. and Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Springer, New York, 1992.
3. Yong, J. M. and Zhou, X. Y., Stochastic Controls, Hamiltonian Systems and HJB Equations, Springer, New York, 1999.
4. Bensoussan, A., Stochastic Control of Partially Observable Systems, Cambridge University Press, Cambridge, 1992.
5. Zhu, W. Q. and Ying, Z. G., 'Optimal nonlinear feedback control of quasi Hamiltonian systems', Science in China, Series A 42, 1999, 1213-1219.
6. 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.
7. Zhu, W. Q. and Yang, Y. Q., 'Stochastic averaging of quasi non-integrable Hamiltonian systems', ASME, Journal of Applied Mechanics 64, 1997, 157-164.
8. 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.
9. 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.
10. Zhu, W. Q., Ying, Z. G., Ni, Y. Q., and Ko, J. M., 'Optimal nonlinear stochastic control of hysteretic systems', ASCE, Journal of Engineering Mechanics 126, 2000, 1027-1032.
11. Zhu, W. Q. and Ying, Z. G., 'Nonlinear stochastic optimal control of partially observable linear structures', Engineering Structures 24, 2002, 333-342.
12. Khasminskii, R. Z., 'On the averaging principle for stochastic differential Itô equation', Kibernetika 4, 1968, 260-279 [in Russian].
13. Bankenship, G. and Papanicolaou, G. C., 'Stability and control of stochastic systems with wide-band noise disturbances', SIAM Journal of Applied Mathematics 34, 1978, 437-376.
14. Kushner, H. J., 'Optimality conditions for the average cost per unit time problem with a diffusion model', SIAM Journal of Control and Optimization 16, 1978, 330-346.
15. Kushner, H. J. and Rungguldier, W. J., 'Nearly optimal state feedback control for stochastic systems with wideband noise disturbance', SIAM Journal of Control and Optimization 25, 1987, 298-315.
16. Dimentberg, M. F., Iourtchenko, D. V., and Bratus, A. S., 'Optimal bounded control of steady-state random vibrations', Probabilistic Engineering Mechanics 15, 2000, 381-386.
17. Bratus, A., Dimentberg, M., Iourtchenko, D. V., and Noori, M., 'Hybrid solution method for dynamic programming equations for MDOF stochastic systems', Dynamics and Control 10, 2000, 107-116.
18. Dimentberg, M. F. and Bratus, A. S., 'Bounded parametric control of random vibrations', Proceedings of the Royal Society of London, Series A 456, 2000, 2351-2363.
19. Zhu, W. Q. and Lei, Y., 'First passage time for state transition of randomly excited systems', in Bulletin of the International Statistical Institute, Proceedings of the 47th Session, Vol. LIII, Book 3 (Invited Papers), August 27-September 6, 1989, pp. 517-531.
20. 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.
21. Gan, C. B. and Zhu, W. Q., 'First-passage failure of quasi-non-integrable-Hamiltonian system', International Journal of Non-Linear Mechanics 36, 2001, 209-220.