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Parameter Estimation for Nonlinear Functions Related to System Responses

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  • Control Theory and Applications
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Abstract

This paper considers the parameter estimation problem of nonlinear models, which are related to the impulse or step response functions of linear time-invariant (LTI) dynamical systems, based on the response data. In terms of the nonlinear characteristic of the models, the nonlinear dynamical optimization scheme is adopted for obtaining the system parameter estimates. By constructing a gradient criterion function, a gradient recursion algorithm is derived. In order to overcome the difficulty of determining the step-size in the gradient recursion algorithm, a trying method and a numerical approach are proposed to achieve the step-size. On this basis, a stochastic gradient estimation method is presented by using a recursive step-size. Furthermore, a multi-innovation stochastic gradient method is deduced for enhancing the estimation accuracy by using the dynamical window data. Finally, a dynamical length stochastic gradient estimation technique is offered to obtain more accurate parameter estimates by using dynamical length measured data from the step response. The examples are provided to examine the algorithm performance and the simulation results indicate that the presented approaches are effective.

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Authors and Affiliations

  1. School of Internet of Things and Artificial Intelligence, Wuxi Vocational Institute of Commerce, Wuxi, 214153, China

    Ling Xu

  2. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159, China

    Ling Xu

  3. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China

    Ling Xu

  4. School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, 430068, China

    Ling Xu

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  1. Ling Xu
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The author declares that there is no conflict of interests regarding the publication of this paper.

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 was a Post-Doctoral Fellow at the Jiangnan University from 2016 to 2020 and is currently a Professor. She is a Colleges and Universities “Blue Project” Young Teacher (Jiangsu, China). Her research interests include process control, parameter estimation, and signal modeling.

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This work was supported by the National Natural Science Foundation of China (No. 61873111).

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Xu, L. Parameter Estimation for Nonlinear Functions Related to System Responses. Int. J. Control Autom. Syst. 21, 1780–1792 (2023). https://doi.org/10.1007/s12555-021-1028-6

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