Acta Mechanica Solida Sinica

, Volume 22, Issue 2, pp 143–151 | Cite as

Stochastic optimal vibration control of partially observable nonlinear quasi Hamiltonian systems with actuator saturation

  • Ronghua Huan
  • Lincong Chen
  • Weiliang Jin
  • Weiqiu Zhu
Article

Abstract

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First, a controlled partially observable nonlinear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Itô stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.

Key words

nonlinear system random excitations optimal control partially observation actuator saturation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Fleming, W.H. and Soner, H.M., Controlled Markov Processes and Viscosity Solutions. New York: Springer, 1993.MATHGoogle Scholar
  2. [2]
    Yong, J.M., and Zhou, X.Y., Stochastic Control, Hamiltonian Systems and HJB Equations. New York: Springer, 1999.MATHGoogle Scholar
  3. [3]
    Zhu, W.Q. and Ying, Z.G., Nonlinear stochastic optimal control of partially observable linear structures. Journal of Engineering and Structures, 2002, 24: 333–342.CrossRefGoogle Scholar
  4. [4]
    Zhu W.Q. and Ying, Z.G., On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems. Journal of Zhejiang University Science A, 2004, 5: 1313–1317.CrossRefGoogle Scholar
  5. [5]
    Crespo, L.G. and Sun, J.Q., On the feedback Linearization of the Lorenz system. Journal of Vibration and Control, 2004, 10: 85–100.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Crespo, L.G. and Sun, J.Q., Non-linear stochastic control via stationary response design. Probabilistic Engineering Mechanics, 2003, 18: 79–86.CrossRefGoogle Scholar
  7. [7]
    Elbeyli, O. and Sun, J.Q., A stochastic averaging approach for feedback control design of nonlinear systems under random excitations. Journal of Vibration and Acoustics, 2002, 124: 561–565.CrossRefGoogle Scholar
  8. [8]
    Bratus, A., Dimentberg M. and Iourtchenko, D., Optimal bounded response control for a second-order system undera white-noise excitation. Journal of Vibration and control, 2000, 6: 741–755.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Iourtchenko, D.V., Stochastic optimal bounded control for a system with the boltz cost function. Journal of vibration and control, 2000, 6: 1195–1204.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Dimentberg, M.F., Iourtchenko, D.V. and Bratus, A.S., Optimal bounded control of steady-state random vibrations. Probabilistic Engineering Mechanics, 2000, 15: 381–386.CrossRefGoogle Scholar
  11. [11]
    Dimentberg, M.F. and Bratus, A.S., Bounded parametric control of random vibrations. Proceedings of the Royal Society of London Series A, 2000, 456: 2351–2363.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Zhu, W.Q. and Ying, Z.G., Optimal nonlinear feedback control of quasi Hamiltonian systems. Science in China Series A, 1999, 42: 1213–1219.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Zhu, W.Q., Ying, Z.G. and Soong, T.T., An optimal nonlinear feedback control strategy for randomly excited structural systems. Nonlinear Dynamics, 2003, 24: 31–51.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Ying, Z.G., Zhu, W.Q. and Soong, T.T., A stochastic optimal semi-active control strategy for ER/MR dampers. Journal of Sound and Vibration, 2003, 259: 45–62.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Ying, Z.G. and Zhu, W.Q., Stochastic optimal control of hysteretic systems under externally and parametrically random excitations. Acta Mechanica Solida Sinica, 2003, 16(1): 61–66.Google Scholar
  16. [16]
    Deng, M.L., Hong, M.C. and Zhu, W.Q., Stochastic Optimal control for the response of quasi non-integrable Hamiltonian systems. Acta Mechanica Solida Sinica, 2003, 16(4): 313–320.Google Scholar
  17. [17]
    Zhu, W.Q. and Deng, M.L., Optimal bounded control for minimizing the response of quasi non-integrable Hamiltonian systems. Nonlinear Dynamics, 2004, 35: 81–100.MathSciNetCrossRefGoogle Scholar
  18. [18]
    Zhu, W.Q. and Deng, M.L., Optimal bounded control for minimizing the response of quasi integrable Hamiltonian systems. International Journal of Non-linear Mechanic, 2004, 39: 1535–1546.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Zhu, W.Q., Huang, Z.L. and Yang, Y.Q., Stochastic averaging of quasi integrable Hamiltonian systems. ASME Journal of Applied Mechanics, 1997, 64: 975–984.MathSciNetCrossRefGoogle Scholar
  20. [20]
    Zhu, W.Q. and Yang, Y.Q., Stochastic averaging of quasi non-integrable Hamiltonian systems. ASME Journal of Applied Mechanics, 1997, 64: 157–164.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Charalambous, C.D. and Elliott, R.J., Certain nonlinear partially observable stochastic optimal control problems with explicit control laws equivalent to LEQG/LQG problems. IEEE Trans Automatic Control, 1997, 42: 482–497.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Charalambous, C.D. and Elliott, R.J., Classes of nonlinear partially observable stochastic optimal control problems with explicit optimal control laws. SIAM Journal on Control and Optimization, 1998, 36: 542–578.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  • Ronghua Huan
    • 1
  • Lincong Chen
    • 1
  • Weiliang Jin
    • 2
  • Weiqiu Zhu
    • 1
  1. 1.Department of MechanicsZhejiang UniversityHangzhouChina
  2. 2.College of Civil Engineering and ArchitectureZhejiang UniversityHangzhouChina

Personalised recommendations