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Linear Optimal Estimation for Discrete-time and Continuous-time Systems with Multiple Measurement Delays

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  • Control Theory and Applications
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Abstract

In this paper, we investigate the linear optimal estimation problems of discrete-time and continuous-time systems with multiple state delays in measurements. For discrete-time systems, we obtain the linear optimal estimation of state by direct calculation of optimal gain in terms of the solution to a retarded Riccati-like difference equation instead of a group of Riccati difference equations. For continuous-time systems, we also obtain the analytical expression of linear optimal estimation without resorting to Riccati partial differential equations. All the Riccati equations are of the same dimension as the system to be estimated and the computational cost is much saved. Infinite horizon case is also studied by stability analysis. Kalman filter can be recovered from our result when delays disappear. A numerical example is provided to demonstrate the results.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, 17923 Jingshi Road, Jinan, Shandong, 250061, China

    Na-Na Jin, Shuai Liu & Huan-Shui Zhang

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  1. Na-Na Jin
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  2. Shuai Liu
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  3. Huan-Shui Zhang
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Correspondence to Shuai Liu.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor DaeEun Kim under the direction of Editor Hamid Reza Karimi. This work is supported by the National Natural Science Foundation of China under Grants 61633014, U1701264, and the foundation for innovative research groups of National Natural Science Foundation of China (61821004).

Na-Na Jin received her B.E. and M.E. degrees in pure mathematics from School of Mathematical Sciences, University of Jinan, in 2014 and 2017, respectively. She is now working toward a Ph.D. degree in the School of Control Science and Engineering, Shandong University. Her research interests include optimal estimation and control, time-delay systems.

Shuai Liu received his B.E. and M.E. degrees in control theory and engineering from Shandong University in 2004 and 2007, respectively, and his Ph.D. degree in electrical and electronic engineering from Nanyang Technological University, Singapore, in 2012. He was a senior research fellow with Berkeley education alliance for research in Singapore (BEARS) from 2011 to 2017. Since 2017, he has been with the School of Control Science and Engineering, Shandong University, China. His research interests include optimal estimation and control, time-delay systems, fault detection and estimation.

Huan-Shui Zhang received his M.Sc. and Ph.D. degrees in control theory from Heilongjiang University, and Northeastern University, in 1991 and 1997, respectively. He worked as a postdoctoral fellow at Nanyang Technological University from 1998 to 2001 and as a Research Fellow at Hong Kong Polytechnic University from 2001 to 2003. He is currently a Changjiang Professorship at Shandong University. He was a Professor at the Harbin Institute of Technology from 2003 to 2006. He also held visiting appointments as a Research Scientist and Fellow with Nanyang Technological University, Curtin University of Technology, and Hong Kong City University from 2003 to 2006. His interests include optimal estimation and control, time-delay systems, stochastic systems, signal processing and wireless sensor networked systems.

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Jin, NN., Liu, S. & Zhang, HS. Linear Optimal Estimation for Discrete-time and Continuous-time Systems with Multiple Measurement Delays. Int. J. Control Autom. Syst. 19, 1194–1204 (2021). https://doi.org/10.1007/s12555-020-0167-5

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  • DOI: https://doi.org/10.1007/s12555-020-0167-5

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