Feedback stabilization of Quasi-integrable Hamiltonian systems

Journal of Applied Mechanics, Transactions ASME

Volumn 70, Issue 1, 2003, Pages 129-136

  Zhu, W Q ^a   Huang, Z L ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; HAMILTONIANS; INTEGRAL EQUATIONS; LYAPUNOV METHODS; STOCHASTIC CONTROL SYSTEMS;

FEEDBACK STABILIZATION;

FEEDBACK CONTROL;

EID: 0037233454     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1483833     Document Type: Conference Paper

References (23)

1. Kushner, J., 1967, Stochastic Stability and Control, Academic Press, New York.
2. Khasminskii, R. Z., 1980, Stochastic Stability of Differential Equation, Sijthoff & Noordhoff, Alphen ann den Rijn.
3. Florchinger, D., 1995, "Lyapunov-Like Technique for Stochastic Stability," SIAM J. Control Optim., 33, pp. 1151-1169.
4. Florchinger, D., 1997, "Feedback Stabilization of Affine in the Control Stochastic Differential Systems by the Control Lyapunov Function Method," SIAM J. Control Optim., 35, pp. 500-511.
5. Pan, Z., and Basar, T., 1999, "Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion," SIAM J. Control Optim., 37, pp. 957-995.
6. Deng, H., and Krstic, M., 1997, "Stochastic Nonlinear Stabilization - Part II: Inverse Optimality," Syst. Control Lett., 32, pp. 151-159.
7. Deng, H., and Krstic, M., 1999, "Output-Feedback Stochastic Nonlinear Stabilization," IEEE Trans. Autom. Control, 44, pp. 328-333.
8. Deng, H., and Krstic, M., 2000, "Output-Feedback Stabilization of Stochastic Nonlinear Systems Driven by Noise of Unknown Covariance." Syst. Control Lett., 39, pp. 173-182.
9. Tsinias, J., 1998, "Stochastic Input-to-State Stability and Applications to Global Feedback Stabilization," Int. J. Control, 71, pp. 905-930.
10. Oseledec, V. I., 1968, "A Multiplicative Ergodic Theorem: Lyapunov Characteristic Number for Dynamical Systems," Trans. Moscow Mathematical Society, 19, pp. 197-231.
11. Khasminskii, R. Z., 1967, "Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems," Theor. Probab. Appl., 12, pp. 144-147.
12. Ariaratnam, S. T., and Xie, W. C., 1992, "Lyapunov Exponents and Stochastic Stability of Coupled Linear Systems Under Real Noise Excitation." ASME J. Appl. Mech., 59, pp. 664-673.
13. Zhu, W. Q., and Huang, Z. L., 1999, "Lyapunov Exponents and Stochastic Stability of Quasi-Integrable-Hamiltonian Systems," ASME J. Appl. Mech., 66, pp. 211-217.
14. Zhu, W. Q., Huang, Z. L., and Yang, Y. Q., 1997, "Stochastic Averaging of Quasi-Integrable-Hamiltonian Systems," ASME J. Appl. Mech., 64, pp. 975-984.
15. Huang, Z. L., and Zhu, W. Q., 2000, "Lyapunov Exponent and Almost Sure Asymptotic Stability of Quasi-Linear Gyroscopic Systems," Int. J. Non-Linear Mech., 35. pp. 645-655.
16. Zhu, W. Q., and Ying, Z. G., 1999, "Optimal Nonlinear Feedback Control of Quasi Hamiltonian Systems," Sci. China, Ser. A: Math., Phys., Astron., 42, pp. 1213-1219.
17. Zhu, W. Q., Ying, Z. G., Ni, Y. Q., and Ko, J. M., 2000, "Optimal Nonlinear Stochastic Control of Hysteretic Systems," J. Eng. Mech., 126, pp. 1027-1032.
18. Zhu, W. Q., Ying, Z. G., and Soong, T. T., 2001, "An Optimal Nonlinear Feedback Control Strategy for Randomly Excited Structural Systems," Nonlinear Dyn., 24, pp. 31-51.
19. Zhu, W. Q., and Yang, Y. Q., 1997, "Stochastic Averaging of Quasi-Nonintegrable-Hamiltonian Systems," ASME J. Appl. Mech., 64, pp. 157-164.
20. Wong. E., and Zakai, M., 1965, "On the Relation Between Ordinary and Stochastic Equations," Int. J. Eng. Sci., 3, pp. 213-229.
21. Khasminskii, R. Z., 1968, "On the Averaging Principle for Stochastic Differential Equation," Kibernetika, 4, pp. 260-279 (in Russian).
22. Kushner, J., 1978, "Optimality Conditions for the Average Cost Per Unit Time Problem With a Diffusion Model," SIAM J. Control Optim., 16, pp. 330-346.
23. Lin, Y. K., and Cai, G. Q., 1995, Probabilistic Structure Dynamics, Advanced Theory and Applications, McGraw-Hill, New York.