Abstract
This paper presents the information filter, which is developed in filtered forms, for time-delay systems which include continuous-time case and discrete-time case. By introducing delay-free observation, the optimal filtering problems for time-delay systems can be converted into multiple steps prediction problems for delay-free systems. Then, the recursive forms for optimal filter are given via innovation approach in Hilbert space. Furthermore, the information filter in Riccati recursions can be derived by using the matrix inversion Lemma to optimal filtering formulas. Finally, the distributed Kalman filter for time-delay systems is designed based on information filter developed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Hassibi, H. A. Sayed, and T. Kailath, Indefinite Quadratic Estimation and Control: A Unified Approach to H2 and H ∞ Theories, SIAM Studies in Applied Mathematics Series, 1998.
B. D. O. Anderson and J. B. Moore, Optimal Filtering, Englewood, Prentice-Hall, Cliffs, NJ, 1979.
D. Simon, Optimal State Estimation-Kalman, H∞ and Nonlinear Approaches, John Wiley and Sons, New Jersey, 2006.
A. Ahmad, M. Gani, and F. Yang, “Decentralized robust Kalman filtering for uncertain stochastic systems over heterogeneous sensor networks,” Signal Process., vol. 88, no. 8, pp. 1919–1928, 2008.
Y. Zhang, C. Soh, and W. Chen, “Robust informaiton filter for decentralized estimation,” Automatica, vol. 41, no. 12, pp. 2141–2146, 2005.
S. Ouic, J. Sijs, and P. P. J. van den Bosch, “Optimal decentralized Kalman filter,” Proc. of 17th Mediterranean Conf. on Contr. and Auto., pp. 803–808, 2009.
M. H. Terra, J.Y. Ishihara, and A. C. Padoan, “Information filtering and array algorithms for descriptor systems subject to parameter uncertainties,” IEEE Trans. Signal Process., vol. 55, no. 1, pp. 1–9, 2007.
M. H. Terra, J.Y. Ishihara, and G. Jesus, “Information filtering and array algorithms for discrete-time Markovian jump linear systems,” Proc. of the American Contr. Conf., pp. 1062–1066, 2007.
G. Jesus, J. Y. Ishihara, and M. H. Terra, “Information filtering and array algorithms for discrete-time Markovian jump linear systems subject to parameter uncertainties,” Proc. of the American Contr. Conf., pp. 605–610, 2010.
H. Hashemipour, S. Roy, and A. Laub, “Decentralized structures for parallel Klaman filtering,” IEEE Trans. Autom. Control, vol. 33, no. 1, pp. 88–99, 1988.
M. Basin, M. A. Alcorta-Garcia, and A. Alanis-Duran, “Optimal filtering for linear systems with state and multiple observation delays,” Proc. of American Contr. Conf., pp. 991–996, Minnesota, 2006.
H. Zhao and P. Cui, “Risk sensitive fixed point smoothing estimation for linear discrete-time systems with multiple output delays,” Jour. of Sys. Sci. and Complexity, vol. 26, no. 2, pp. 137–156, 2013.
N. Briggs and R. Vinter, “Linear filtering for time-delay systems,” Jour. Math. Contr. Inform., vol. 6, no. 2, pp. 167–178, 1989.
H. Kwakernaak, “Optimal filtering in linear systems with time delays,” IEEE Trans. Autom. Control, vol. 12, no. 2, pp. 169–173, 1967.
Y. Song, V. Shin, and M. Jeon, “Distributed fusion receding horizon filtering for uncertain linear stochastic systems with time-delay sensors,” Jour. of the Franklin Ins., vol. 349, no. 3, pp. 928–946, 2012.
H. Zhang, and L. Xie, Control and Estimation of Systems with Input/Output Delays, Springer-Verlag, Berlin Heidelberg, 2007.
H. Huang, G. Feng, and J. Cao, “An LMI approach to delay-dependent state estimation for delayed neural networks,” Neurocomputing, vol. 71, no. 13-15, pp. 2857–2867, 2008.
B. Chen, L. Yu, and W. A. Zhang, “Robust Kalman filtering for uncertain state delay systems with random observation delays and missing measurements,” IET Contr. Theory Applica., vol. 5, no. 17, pp. 1945–1954, 2011.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Chang Kyung Ryoo under the direction of Editor Yoshito Ohta. This work was supported by National Natural Science Foundation (NNSF) of China under Grants 61273124, 61573220, Doctoral Foundation of Taishan University under Grant Y11-2-02, and A Project of Shandong Province Higher Education Science and Technology Program under Grant J12LN90.
Hongguo Zhao received his M.E. degree in control science and engineering from the Changsha University of Science and Technology in 2005, and his Ph.D. degree in control science and engineering from the Shandong University in 2008. Currently, he is an associate professor in School of Information Science and Technology at Taishan University. His research interests include optimal estimation, signal processing, timedelay systems, robust control.
Wei Wang received his Ph.D. degree in control science and engineering from Shenzhen Graduate School, Harbin Institute of Technology, in 2010. He is currently an associate professor at Shandong University, Jinan Shandong, China. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.
Rights and permissions
About this article
Cite this article
Zhao, H., Wang, W. Information filtering for time-delay systems. Int. J. Control Autom. Syst. 15, 248–257 (2017). https://doi.org/10.1007/s12555-015-0152-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-015-0152-6