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Volumn 33, Issue 2, 2003, Pages 209-224

Stochastic Stabilization of Quasi-Partially Integrable Hamiltonian Systems by Using Lyapunov Exponent

Author keywords

Dynamical programming; Lyapunov exponent; Nonlinear system; Stochastic averaging; Stochastic excitation; Stochastic optimal control; Stochastic stabilization

Indexed keywords

ASYMPTOTIC STABILITY; DYNAMIC PROGRAMMING; FEEDBACK CONTROL; HAMILTONIANS; OPTIMAL CONTROL SYSTEMS;

EID: 0142184978     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026010007067     Document Type: Article
Times cited : (17)

References (22)
  • 3
    • 0031099377 scopus 로고    scopus 로고
    • Feedback stabilization of affine in the control stochastic differential systems by the control Lyapunov function method
    • Florchinger, D., 'Feedback stabilization of affine in the control stochastic differential systems by the control Lyapunov function method', SIAM Journal of Control and Optimization 35, 1997, 500-511.
    • (1997) SIAM Journal of Control and Optimization , vol.35 , pp. 500-511
    • Florchinger, D.1
  • 5
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem: Lyapunov characteristic number for dynamical systems
    • Oseledec, V. I., 'A multiplicative ergodic theorem: Lyapunov characteristic number for dynamical systems', Transactions of Moscow Mathematical Society 19, 1968, 197-231.
    • (1968) Transactions of Moscow Mathematical Society , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 6
    • 0001549366 scopus 로고
    • Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems
    • Khasminskii, R. Z., 'Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems', Theory of Probability and Application 12, 1967, 144-147.
    • (1967) Theory of Probability and Application , vol.12 , pp. 144-147
    • Khasminskii, R.Z.1
  • 7
    • 0026917425 scopus 로고
    • Lyapunov exponents and stochastic stability of coupled linear systems under real noise excitation
    • Ariaratnam, S. T. and Xie, W. C., 'Lyapunov exponents and stochastic stability of coupled linear systems under real noise excitation', ASME Journal of Applied Mechanics 59, 1992, 664-673.
    • (1992) ASME Journal of Applied Mechanics , vol.59 , pp. 664-673
    • Ariaratnam, S.T.1    Xie, W.C.2
  • 8
    • 0033100332 scopus 로고    scopus 로고
    • Lyapunov exponents and stochastic stability of quasi-integrable-Hamiltonian systems
    • Zhu, W. Q. and Huang, Z. L., 'Lyapunov exponents and stochastic stability of quasi-integrable-Hamiltonian systems', ASME Journal of Applied Mechanics 66, 1999, 211-217.
    • (1999) ASME Journal of Applied Mechanics , vol.66 , pp. 211-217
    • Zhu, W.Q.1    Huang, Z.L.2
  • 10
    • 0001761644 scopus 로고
    • A limit theorem for the solutions of differential equations with random right hand sides
    • 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.
    • (1966) Theory of Probability and Applications , vol.11 , pp. 390-406
    • Khasminskii, R.Z.1
  • 11
    • 0017972055 scopus 로고
    • Stability and control of stochastic systems with wide-band noise disturbances
    • Blankenship, G. and Papanicolaou, G. C., 'Stability and control of stochastic systems with wide-band noise disturbances', SIAM Journal of Applied Mathematics 34, 1978, 437-476.
    • (1978) SIAM Journal of Applied Mathematics , vol.34 , pp. 437-476
    • Blankenship, G.1    Papanicolaou, G.C.2
  • 12
    • 0023306016 scopus 로고
    • Nearly optimal state feedback controls for stochastic systems with wideband noise disturbances
    • Kushner, H. D. 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.
    • (1987) SIAM Journal of Control and Optimization , vol.25 , pp. 298-315
    • Kushner, H.D.1    Runggaldier, W.2
  • 13
    • 0035298030 scopus 로고    scopus 로고
    • Stochastic averaging and Lyapunov exponent of quasi partially integrable Hamiltonian systems
    • 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.
    • (2002) International Journal of Non-linear Mechanics , vol.37 , pp. 419-437
    • Zhu, W.Q.1    Huang, Z.L.2    Suzuki, Y.3
  • 14
    • 0000197126 scopus 로고    scopus 로고
    • Optimal nonlinear feedback control of quasi Hamiltonian systems
    • Zhu, W. Q. and Ying, Z. G., 'Optimal nonlinear feedback control of quasi Hamiltonian systems', Science in China (Series A) 42, 1999, 1213-1219.
    • (1999) Science in China (Series A) , vol.42 , pp. 1213-1219
    • Zhu, W.Q.1    Ying, Z.G.2
  • 16
    • 0035131363 scopus 로고    scopus 로고
    • An optimal nonlinear feedback control strategy for randomly excited structural systems
    • 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.
    • (2001) Nonlinear Dynamics , vol.24 , pp. 31-51
    • Zhu, W.Q.1    Ying, Z.G.2    Soong, T.T.3
  • 17
    • 0031100992 scopus 로고    scopus 로고
    • Stochastic averaging of quasi non-integrable Hamiltonian systems
    • Zhu, W. Q. and Yang, Y. Q., 'Stochastic averaging of quasi non-integrable Hamiltonian systems', ASME Journal of Applied Mechanics 64, 1997, 157-164.
    • (1997) ASME Journal of Applied Mechanics , vol.64 , pp. 157-164
    • Zhu, W.Q.1    Yang, Y.Q.2
  • 18
    • 0000761056 scopus 로고    scopus 로고
    • Stochastic averaging of quasi integrable Hamiltonian systems
    • 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.
    • (1997) ASME Journal of Applied Mechanics , vol.64 , pp. 975-984
    • Zhu, W.Q.1    Huang, Z.L.2    Yang, Y.Q.3
  • 21
    • 0000182826 scopus 로고
    • On the averaging principle for stochastic equation
    • in Russian
    • Khasminskii, R. Z., 'On the averaging principle for stochastic equation', Kibernetika 4, 1968, 260-279 [in Russian].
    • (1968) Kibernetika , vol.4 , pp. 260-279
    • Khasminskii, R.Z.1
  • 22
    • 0017949910 scopus 로고
    • Optimality conditions for the average cost per unit time problem with a diffusion model
    • Kushner, 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.
    • (1978) SIAM Journal of Control and Optimization , vol.16 , pp. 330-346
    • Kushner, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.