参考文献:1. K. K. Biswas, A. K. Mahalanabis. An approach to fixed-point smoothing problems. / IEEE Transactions on Aerospace and Electronic Systems, 1972, 5(5): 676鈥?82. CrossRef 2. S. Nakamori. Design of extended recursive Wiener fixed-point smoother and filter in discrete-time stochastic systems. / Digital Signal Processing, 2007, 17(1): 360鈥?70. CrossRef 3. T. Kailath, A. H. Sayed, B. Hassibi. / Linear Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1999. 4. B. D. O. Anderson, J. B. Moore. / Optimal Filtering. Englewood. Cliffs, NJ: Prentice-Hall, 1979. 5. Y. Theodor, U. Shaked. Game theory approach to H / 鈭?/em>-optimal discrete-time fixed-point and fixed-lag smoothing. / IEEE Transactions on Automatic Control, 1994, 39(9): 1944鈥?948. CrossRef 6. A. H. Carazo, J. L. Prez, J. D. J. Lpez, et al. Recursive fixed-point smoothing algorithm from covariances based on uncertain observations with correlation in the uncertainty. / Applied Mathematics and Computation, 2008, 203(1): 243鈥?51. CrossRef 7. M. Farooq, D. R. Balasubramanian. Fixed-interval smoothing of linear discrete systems with multiple time delays. / IEEE Transactions on Automatic Control, 1976, 21(2): 273鈥?75. CrossRef 8. H. Zhang, L. Xie. / Control and Estimation of Systems with Input/Output Delays. Berlin: Springer-Verlag, 2007. 9. K. K. Biswas, A. K. Mahalanabis. Optimal fixed lag smoothing for time delayed system with colored noise. / IEEE Transactions on Automatic Control, 1972, 17(3): 387鈥?88. CrossRef 10. D. W. Repperger, A. J. Koivo. On stable, forward, filtering and fixed-lag smoothing in a class of systems with time delays. / IEEE Transactions on Automatic Control, 1974, 19(3): 266鈥?68. CrossRef 11. K. K. Biswas, A. K. Mahalanabis. Optimal smoothing for continuoustime systems with multiple time delays. / IEEE Transactions on Automatic Control, 1972, 17(4): 572鈥?74. CrossRef 12. A. Ichikawa. / H 鈭?/sub> control and filtering with initial uncertainty for infinite dimensional systems. / International Journal of Robust and Nonlinear Control, 1996, 6(5): 421鈥?52. CrossRef 13. H. Zhao, H. Zhang, P. Cui. Steady-state optimal filtering for continuous systems with time-delay. / IEEE Signal Processing Letters, 2009, 16(7): 628鈥?31. CrossRef 14. H. Zhao, H. Zhang, C. Zhang. Optimal robust estimation for linear uncertain systems with single delayed measurement. / Acta Automatica Sinica, 2008, 34(2): 202鈥?07. CrossRef
作者单位:Hongguo Zhao (1) (2) Peng Cui (3) Xiaochun Guo (2)
1. Postdoctoral Research Station of School of Mathematics, Shandong University, Jinan Shandong, 250061, China 2. School of Information Science and Technology, Taishan University, Taian Shandong, 271021, China 3. School of Control Science and Engineering, Shandong University, Jinan Shandong, 250061, China
ISSN:1993-0623
文摘
This paper investigates the fixed-point smoothing problems for linear discrete-time systems with multiple time-delays in the observations. The linear discrete-time systems considered have l + 1 output channels. One is instantaneous observation and the others are delayed. The fixed-point smoothers involving recursive algorithm and non-recursive algorithm are designed by using innovation analysis theory without relying on the system augmentation approach. Also, it is further shown that the design of fixed-point smoother comes down to solving l + 1 Riccati equations with the same dimensions as the original systems.