International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

A Robust Adaptive Controller for Markovian Jump Uncertain Nonlinear Systems with Wiener Noises of Unknown Covariance

  • Zhu, Jin (Department of Automation, University of Science and Technology of China) ;
  • Xi, Hong-Sheng (Department of Automation, University of Science and Technology of China) ;
  • Ji, Hai-Bo (Department of Automation, University of Science and Technology of China) ;
  • Wang, Bing (Department of Automation, University of Science and Technology of China)
  • Published : 2007.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

A robust adaptive controller design for a class of Markovian jump parametric -strict-feedback systems is given. The disturbances considered herein include both uncertain nonlinearities and Wiener noises of unknown covariance. And they satisfy some bound-conditions. By using stochastic Lyapunov method in Markovian jump systems, a switching robust adaptive controller was obtained that guarantees global uniform ultimate boundedness of the closed-loop jump system.

Keywords

References

  1. M. Mariton, Jump Linear Systems in Automatic Control, Marcel-Dekker, Inc., New York, 1990
  2. P. Shi, E.-K. Boukas, and R. K. Agarwal, 'Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters,' IEEE Trans. on Automatic Control, vol. 44, no. 8, pp. 1592-1597, 1999 https://doi.org/10.1109/9.780431
  3. M. S. Mahmoud, P. Shi, and A. Ismail, 'Robust Kalman filtering for discrete-time Markovian jump systems with parameter uncertainty,' Journal of Computational and Applied Mathematics, vol. 169, no. 1, pp. 53-69, 2004 https://doi.org/10.1016/j.cam.2003.11.002
  4. Y. Ji and H. J. Chizeck, 'Jump linear quadratic Gaussian control in continuous time,' IEEE Trans. on Automatic Control, vol. 37, no. 12, pp. 1884-1892, 1992 https://doi.org/10.1109/9.182475
  5. M. D. Fragoso, 'Discrete-time jump LQG problem,' International Journal of Systems Science, vol. 20, no. 12, pp. 2539-2545, 1989 https://doi.org/10.1080/00207728908910331
  6. P. Shi, Y. Xia, G. P. Liu, and D. Rees, 'On designing of sliding-mode control for stochastic jump systems,' IEEE Trans. on Automatic Control, vol. 51, no. 1, pp. 97-103, 2006 https://doi.org/10.1109/TAC.2005.861716
  7. M. D. S. Aliyu and E. K. Boukas, '$H_{\infty}$ control for Markovian jump nonlinear systems,' Proc. of the 37th CDC, pp. 766-771, 1998
  8. J. Zhu, H.-S. Xi, H.-B. Ji, and B. Wang, 'Robust adaptive tracking for Markovian jump nonlinear systems with unknown non-linearities,' Discrete Dynamics in Nature and Society, Art. no. 92932, 2006
  9. X. Mao, 'Stability of stochastic differential equations with Markovian switching,' Stochastic Processes and Their Applications, vol. 79, pp. 45-67, 1999 https://doi.org/10.1016/S0304-4149(98)00070-2
  10. C. Yuan and X. Mao, 'Asymptotic stability in distribution of stochastic differential equations with Markovian switching,' Stochastic Processes and Their Applications, vol. 103, pp. 277-291, 2003 https://doi.org/10.1016/S0304-4149(02)00230-2
  11. C. Yuan, and X. Mao, 'Robust stability and controllability of stochastic differential delay equations with Markovian switching,' Automatica, vol. 40, pp. 343-354, 2004 https://doi.org/10.1016/j.automatica.2003.10.012
  12. E. K. Boukas, 'Stabilization of stochastic nonlinear hybrid systms,' Int. J. Innovative Computing, Information and Control, vol. 1, no. 1, pp. 131-141, 2005
  13. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, NY, 1995
  14. M. M. Polycarpou and P. A. Ioannou, 'A robust adaptive nonlinear control design,' Automatica, vol. 32, no. 3, pp.423-427, 1996 https://doi.org/10.1016/0005-1098(95)00147-6
  15. B. Sendal, Stochastic Differential Equations, Springer-Verlag, New York, pp. 49-54, 2000
  16. H. Deng and M. Krstic, 'Stochastic nonlinear stabilizaion-I: A backstepping design,' Systems and Control Letters, vol. 32, pp. 143-150, 1997 https://doi.org/10.1016/S0167-6911(97)00068-6
  17. H. Deng, M. Krstic, and R. J. Williams, 'Stabilization of stochastic nonlinear systems driven by noise of unknown covariance,' IEEE Trans, on Automatic Control, vol. 46, no. 8, pp. 1237-1253, 2001 https://doi.org/10.1109/9.940927