IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i5p428-d230898.html
   My bibliography  Save this article

Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

Author

Listed:
  • Feng Ding

    (School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, China
    College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, China
    School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China)

  • Jian Pan

    (School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, China)

  • Ahmed Alsaedi

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Tasawar Hayat

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

It is well-known that mathematical models are the basis for system analysis and controller design. This paper considers the parameter identification problems of stochastic systems by the controlled autoregressive model. A gradient-based iterative algorithm is derived from observation data by using the gradient search. By using the multi-innovation identification theory, we propose a multi-innovation gradient-based iterative algorithm to improve the performance of the algorithm. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

Suggested Citation

  • Feng Ding & Jian Pan & Ahmed Alsaedi & Tasawar Hayat, 2019. "Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:428-:d:230898
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/5/428/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/5/428/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ling Xu & Feng Ding & Quanmin Zhu, 2019. "Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(1), pages 141-151, January.
    2. Xiao Zhang & Feng Ding & Ling Xu & Ahmed Alsaedi & Tasawar Hayat, 2019. "A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise," Mathematics, MDPI, vol. 7(4), pages 1-17, April.
    3. Chuancun Yin & Chunwei Wang, 2010. "The Perturbed Compound Poisson Risk Process with Investment and Debit Interest," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 391-413, September.
    4. Fengying Ma & Yankai Yin & Min Li, 2019. "Start-Up Process Modelling of Sediment Microbial Fuel Cells Based on Data Driven," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    5. Yin, Chuancun & Wen, Yuzhen, 2013. "Optimal dividend problem with a terminal value for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 769-773.
    6. Jian Pan & Hao Ma & Xiao Jiang & Wenfang Ding & Feng Ding, 2018. "Adaptive Gradient-Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique," Complexity, Hindawi, vol. 2018, pages 1-11, July.
    7. Bo Fu & Chenxi Ouyang & Chaoshun Li & Jinwen Wang & Eid Gul, 2019. "An Improved Mixed Integer Linear Programming Approach Based on Symmetry Diminishing for Unit Commitment of Hybrid Power System," Energies, MDPI, vol. 12(5), pages 1-14, March.
    8. Chuancun Yin & Yuzhen Wen, 2013. "Optimal dividends problem with a terminal value for spectrally positive Levy processes," Papers 1302.6011, arXiv.org.
    9. Yin, Chuancun & Wen, Yuzhen & Zhao, Yongxia, 2014. "On The Optimal Dividend Problem For A Spectrally Positive Lévy Process," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 635-651, September.
    10. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    11. Jiling Ding, 2017. "The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise," Complexity, Hindawi, vol. 2017, pages 1-11, October.
    12. Tiezhou Wu & Xiao Shi & Li Liao & Chuanjian Zhou & Hang Zhou & Yuehong Su, 2019. "A Capacity Configuration Control Strategy to Alleviate Power Fluctuation of Hybrid Energy Storage System Based on Improved Particle Swarm Optimization," Energies, MDPI, vol. 12(4), pages 1-11, February.
    13. Chuancun Yin & Yuzhen Wen & Yongxia Zhao, 2013. "On the optimal dividend problem for a spectrally positive Levy process," Papers 1302.2231, arXiv.org, revised Mar 2014.
    14. Yin, Chuancun & Yuen, Kam Chuen, 2011. "Optimality of the threshold dividend strategy for the compound Poisson model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1841-1846.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lijuan Wan & Ximei Liu & Feng Ding & Chunping Chen, 2019. "Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    2. Hao Ma & Jian Pan & Lei Lv & Guanghui Xu & Feng Ding & Ahmed Alsaedi & Tasawar Hayat, 2019. "Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    3. Junxia Ma & Qiuling Fei & Fan Guo & Weili Xiong, 2019. "Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems," Mathematics, MDPI, vol. 7(12), pages 1-16, November.
    4. Zhang, Aili & Chen, Ping & Li, Shuanming & Wang, Wenyuan, 2022. "Risk modelling on liquidations with Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    5. Boxma, Onno & Frostig, Esther, 2018. "The dual risk model with dividends taken at arrival," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 83-92.
    6. Jos'e-Luis P'erez & Kazutoshi Yamazaki, 2016. "Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities," Papers 1612.02444, arXiv.org, revised Jan 2018.
    7. Aili Zhang & Ping Chen & Shuanming Li & Wenyuan Wang, 2020. "Risk Modelling on Liquidations with L\'{e}vy Processes," Papers 2007.01426, arXiv.org.
    8. Chuancun Yin & Kam Chuen Yuen, 2014. "Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs," Papers 1409.0407, arXiv.org.
    9. Xiao Zhang & Feng Ding & Ling Xu & Ahmed Alsaedi & Tasawar Hayat, 2019. "A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise," Mathematics, MDPI, vol. 7(4), pages 1-17, April.
    10. Wenyuan Wang & Yuebao Wang & Ping Chen & Xueyuan Wu, 2022. "Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 924-965, September.
    11. Benjamin Avanzi & Debbie Kusch Falden & Mogens Steffensen, 2022. "Stable Dividends under Linear-Quadratic Optimization," Papers 2210.03494, arXiv.org.
    12. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    13. Benjamin Avanzi & Jos'e-Luis P'erez & Bernard Wong & Kazutoshi Yamazaki, 2016. "On optimal joint reflective and refractive dividend strategies in spectrally positive L\'evy models," Papers 1607.01902, arXiv.org, revised Nov 2016.
    14. Chongrui Zhu, 2021. "Optimality of threshold strategies for spectrally negative Levy processes and a positive terminal value at creeping ruin," Papers 2107.06841, arXiv.org, revised Jan 2023.
    15. Florin Avram & Dan Goreac & Juan Li & Xiaochi Wu, 2021. "Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model," Mathematics, MDPI, vol. 9(9), pages 1-27, April.
    16. Czarna, Irmina & Pérez, José-Luis & Yamazaki, Kazutoshi, 2018. "Optimality of multi-refraction control strategies in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 148-160.
    17. Gordienko, E. & Vázquez-Ortega, P., 2018. "Continuity inequalities for multidimensional renewal risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 48-54.
    18. Zhang, Jiannan & Chen, Ping & Jin, Zhuo & Li, Shuanming, 2021. "On a class of non-zero-sum stochastic differential dividend games with regime switching," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    19. Pérez, José-Luis & Yamazaki, Kazutoshi, 2017. "On the optimality of periodic barrier strategies for a spectrally positive Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 1-13.
    20. Piotr Jaworski & Kamil Liberadzki & Marcin Liberadzki, 2021. "On Write-Down/ Write-Up Loss Absorbing Instruments," European Research Studies Journal, European Research Studies Journal, vol. 0(1), pages 1204-1219.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:428-:d:230898. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.