Risk-sensitive filtering for discrete-time systems with time-varying delay

Abstract

In this paper, the risk-sensitive filtering problem with time-varying delay is investigated. The problem is transformed into Krein space as an equivalent optimisation problem. The observations with time-varying delays are restructured as ones with multiple constant delays by defining a binary variable model with respect to the arrival process of observations, containing the same state information as the original. Finally, the reorganised innovation analysis approach in Krein space allows the solution to the proposed risk-sensitive filtering in terms of the solutions to Riccati and matrix difference equations.

Keywords:

• risk-sensitive filtering
• time-varying delay
• reorganised innovation analysis
• singular matrix difference equation

Acknowledgements

This work was supported by the National Nature Science Foundation of China (Grant Nos. 61104050, 61203029, 61273124), the Natural Science Foundation of Shandong Province (Grant No. ZR2011FQ020) and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120131120058).

Additional information

Notes on contributors

Wei Wang

Wei Wang received the PhD degree in Control Science and Engineering from Shenzhen Graduate School, Harbin Institute of Technology, in 2010. He is currently a Lecturer at Shandong University, Jinan Shandong, China. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.

Chunyan Han

Chunyan Han received her PhD degree in Control Theory and Control Engineering from Shandong University in 2010. She is currently a Lecturer at the School of Electrical Engineering, University of Jinan. Her research interest covers optimal control and estimation, time-delay systems and Markov jump linear systems.

Hongguo Zhao

Hongguo Zhao received the ME degree in Control Science and Engineering from the Changsha University of Science and Technology in 2005 and the PhD degree in Control Science and Engineering from the Shandong University in 2008. Currently, he is an Associate Professor in the School of Information Science and Technology at Taishan University, Taian Shandong, China. His research interests include optimal estimation, signal processing, time-delay systems and robust control.