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Extended Gradient-based Iterative Algorithm for Bilinear State-space Systems with Moving Average Noises by Using the Filtering Technique

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Abstract

This paper develops a filtering-based iterative algorithm for the combined parameter and state estimation problems of bilinear state-space systems, taking account of the moving average noise. In order to deal with the correlated noise and unknown states in the parameter estimation, a filter is chosen to filter the input-output data disturbed by colored noise and a Kalman state observer (KSO) is designed to estimate the states by minimizing the trace of the error covariance matrix. Then, a KSO extended gradient-based iterative (KSO-EGI) algorithm and a filtering based KSO-EGI algorithm are presented to estimate the unknown states and unknown parameters jointly by the iterative estimation idea. The simulation results demonstrate the effectiveness of the proposed algorithms.

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Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, P. R. China

    Siyu Liu, Ling Xu & Feng Ding

  2. School of Physics and Electronic Information Engineering, Henan Polytechic University, Jiaozuo, 454001, P. R. China

    Yanliang Zhang

  3. School of Internet of Things Technology, Wuxi Vocational Institute of Commerce, Wuxi, 214153, P. R. China

    Ling Xu

  4. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi & Tasawar Hayat

Authors
  1. Siyu Liu
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  2. Yanliang Zhang
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  3. Ling Xu
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  4. Feng Ding
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  5. Ahmed Alsaedi
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  6. Tasawar Hayat
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Corresponding authors

Correspondence to Yanliang Zhang or Feng Ding.

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Recommended by Editor Jay H. Lee. This work was supported by Qing Lan Project, the 333 project of Jiangsu Province (No. BRA2018328) and the 111 Project (B12018) and the Opening Project of State Key Laboratory for Intelligent Control and Decision of Complex Systems.

Siyu Liu was born in Jilin Province, China in 1994. She received her B.Sc. degree from Jiangnan University (Wuxi, China) in 2017, and now is a Ph.D. student in the School of Internet of Things Engineering, Jiangnan University (Wuxi, China). Her interests include system modeling, system identification and process control.

Yanliang Zhang received his B.Sc. Degree from Henan University (Kaifeng, China) in 2001. He received a Ph.D. degrees from the School of Electronic Engineering of Xidian University (Xi’an China) in 2011. He was a visiting scholars at Oulu University (Oulu, Finland) from 2016 to 2017. He is currently an associated professor in the School of Physics and Electronic Information Engineering, Henan Polytechnic University (Jiaozuo China). His current research interests include machine vision and signal processing.

Ling Xu was born in Tianjin, China. She received her Master’s and Ph.D. degrees from the Jiangnan University (Wuxi, China), in 2005 and 2015, respectively. She is a Post-Doctoral Fellow at the Jiangnan University and has been an associate professor since 2015. She is a Colleges and Universities “Blue Project” Young Teacher (Jiangsu, China). Her research interests include process control, parameter estimation and signal modeling.

Feng Ding received his B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and his M.Sc. and Ph.D. degrees both from the Tsinghua University, in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University (Wuxi, China) since 2004. His current research interests include model identification and adaptive control. He authored five books on System Identification.

Ahmed Alsaedi obtained his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, mathematical modeling, biomathematics, Newtonian and Non-Newtonian fluid mechanics. He served as the chairman of the mathematics department at KAU and presently he is serving as director of the research program at KAU. Under his great leadership, this program is running quite successfully and it has attracted a large number of highly rated researchers and distinguished professors from all over the world. He is also the head of NAAM international research group at KAU.

Tasawar Hayat was born in Khanewal, Punjab, Distinguished National Professor and Chairperson of Mathematics Department at Quaid-I-Azam University is renowned worldwide for his seminal, diversified and fundamental contributions in models relevant to physiological systems, control engineering. He has a honor of being fellow of Pakistan Academy of Sciences, Third World Academy of Sciences (TWAS) and Islamic World Academy of Sciences in the mathematical Sciences.

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Liu, S., Zhang, Y., Xu, L. et al. Extended Gradient-based Iterative Algorithm for Bilinear State-space Systems with Moving Average Noises by Using the Filtering Technique. Int. J. Control Autom. Syst. 19, 1597–1606 (2021). https://doi.org/10.1007/s12555-019-0831-9

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