International Journal of Control, Automation, and Systems

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

Kalman Filtering for Linear Time-Delayed Continuous-Time Systems with Stochastic Multiplicative Noises

  • Zhang, Huanshui (Shandong University) ;
  • Lu, Xiao (Shandong University of Science and Technology) ;
  • Zhang, Weihai (Shandong University of Science and Technology) ;
  • Wang, Wei (Research Center of Information and Control, Dalian University of Technology)
  • Published : 2007.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

The paper deals with the Kalman stochastic filtering problem for linear continuous-time systems with both instantaneous and time-delayed measurements. Different from the standard linear system, the system state is corrupted by multiplicative white noise, and the instantaneous measurement and the delayed measurement are also corrupted by multiplicative white noise. A new approach to the problem is presented by using projection formulation and reorganized innovation analysis. More importantly, the proposed approach in the paper can be applied to solve many complicated problems such as stochastic $H_{\infty}$ estimation, $H_{\infty}$ control stochastic system with preview and so on.

Keywords

References

  1. B. Hassibi, A. H. Sayed, and T. Kailath, Indefinite-Quadratic Estimation and Control A unified Approach to $H_2$ and $H_{\infty}$ Theories, Prentice-Hall, Englewood. Cliffs, NJ, 1999
  2. O. L. V. Costa and C. S. Kubrusly, 'State-feedback $H_{\infty}$ control for discrete-time infinite-dimensional stochastic bilinear systems,' Journal of Mathematical Systems, Estimation and Control, vol. 6, pp. 1-32, 1996
  3. B. D. O. Anderson and J. B. Moore, Optimal Filtering, Prentice-Hall, Englewood, Cliffs, NJ, 1979
  4. E. Gershon, J. N. Limebeer, U. Shaked, and I. Yaesh, '$H_{\infty}$ filtering of continuous-time linear systems with stochastic parameter uncertainties,' IEEE Trans. on Automatic Control, vol. 46, no. 11, pp. 1788-1793, 2001 https://doi.org/10.1109/9.964692
  5. M. M. Mohler and W. J. Kolodziej, 'An overview of stochastic bilinear control process,' IEEE Trans. on System, Man and Cybernetics, vol. 10, no. 12, pp. 913-919, 1980 https://doi.org/10.1109/TSMC.1980.4308421
  6. V. Dragan and A. Stoica, 'A ${\gamma}$-attenuation$ problem for discrete-time time-varying stochastic systems with multiplicative noise,' Reprint Series of the Institute of Mathematics of Romanian Academy, no. 10, 1998
  7. L. A. Klein, Sensor and Data Fusion Concepts and Applications, SPIE Press, 1999
  8. E. Gershon, U. Shaked, and I. Yaesh, '$H_{\infty}$ control and filtering of discrete-time stochastic systems with multiplicative noise,' Automatica, vol. 37, pp. 409-417, 2001 https://doi.org/10.1016/S0005-1098(00)00164-3
  9. A. E. Bouhtouri, D. Hinriechsen, and A. J. Pritchard, '$H_{\infty}$ type control for discrete-time stochastic system,' Int. J. Robust Nonlinear Control, vol. 9, pp. 923-948, 1999 https://doi.org/10.1002/(SICI)1099-1239(199911)9:13<923::AID-RNC444>3.0.CO;2-2
  10. R. M. Oisiovici and S. L. Cruz, 'State estimation of batch distillation columns using an extended Kalman filter,' Chemical Engineering Science, vol. 55, pp. 4667-4680, 2000 https://doi.org/10.1016/S0009-2509(00)00088-9
  11. E. Fridman, U. Skaked, and L. H. Xie, 'Robust H2 filtering of linear systems with time delays,' Proc. of the 41st IEEE Conf. Decision Contr., USA, Dec. 2002
  12. Y. Chen and B. S. Chen, 'Minimax robust deconvolution filters under stochastic parametric and noise uncertainties,' IEEE Trans. on Signal Processing, vol. 42, pp. 32-45, 1994 https://doi.org/10.1109/78.258119
  13. F. Wang and V. Balakrishnan, 'Robust Kalman filters for linear time-varying systems with stochastic parametric uncertainties,' IEEE Trans. on Signal Processing, vol. 50, no. 4, pp. 803-813, 2002 https://doi.org/10.1109/78.992124
  14. D. Hinrichsen and A. J. Pritchard, 'Stochastic $H_{\infty}$,' SIAM J. Control Optim., vol. 36, pp. 1504-1538, 1998 https://doi.org/10.1137/S0363012996301336
  15. E. Gershon, U. Shaked, and I. Yaesh, 'Robust $H_{\infty}$ estimation of stationary discrete-time linear processes with stochastic uncertainties,' Systems and Control Letters, vol. 45, pp. 257-269, 2002 https://doi.org/10.1016/S0167-6911(01)00183-9
  16. L. H. Xie, Y. Soh, and C. E. de Souza, 'Robust Kalman filtering for uncertain discrete-time systems,' IEEE Trans. on Automatic Control, vol. 39, pp. 1310-1314, 1994 https://doi.org/10.1109/9.293203
  17. C. E. De Souza and L. H. Xie, 'Delay-dependent robust $H_{\infty}$ control of uncertain linear state-delayed systems,' Automatica, vol. 35, pp. 1313-1321, 1999 https://doi.org/10.1016/S0005-1098(99)00025-4
  18. C. E. De Souza, R. Palhares, and P. Peres, 'Robust $H_{\infty}$ filtering for uncertain linear continuous-time systems with multiple time-varying state delays: An LMI approach,' Proc. of the 38th CDC, Phoenix, Arizona, USA, Dec. 1999
  19. M. Mahmound, N. Muthairi, and S. Bingulac, 'Robust Kalman filtering for continuous time-lag systems,' Systems and Control Letters, vol. 38, pp.309-319, 1999 https://doi.org/10.1016/S0167-6911(99)00068-7
  20. W. Zhang, B. Chen, and C. Tseng, 'Robust $H_{\infty}$ filtering for nonlinear stochastic systems,' IEEE Trans. on Signal Processing, vol. 53, no. 2, pp. 589-598, 2005 https://doi.org/10.1109/TSP.2004.840724
  21. X. Lu, L. Xie, H. Zhang, and W. Wang, 'Robust Kalman filtering for discrete-time systems with measurement delay,' IEEE Trans. on Circuits and Systems Part II, vol. 54, no. 6, pp. 522-526, 2007 https://doi.org/10.1109/TCSII.2007.892223
  22. H. Zhang and D. Zhang, 'Finite horizon $H_{\infty}$ fixed-lag smoothing for time-varying continuous systems,' IEEE Trans. on Circuits and Systems Part II, vol. 51, no. 9, pp. 496-499, 2004 https://doi.org/10.1109/TCSII.2004.832771
  23. H. Zhang, X. Lu, and D. Cheng, 'Optimal estimation for continuous-time systems with delayed measurements,' IEEE Trans. on Automatic Control, vol. 51, no. 5, pp. 823-827, 2006 https://doi.org/10.1109/TAC.2006.874983
  24. X. Lu, H. Zhang, W. Wang, and K. L. Teo, 'Kalman filtering for multiple time-delay systems,' Automatica, vol. 41, no. 8, pp. 1455-1461, 2005 https://doi.org/10.1016/j.automatica.2005.03.018