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Aitken-Based Stochastic Gradient Algorithm for ARX Models with Time Delay

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Abstract

This paper proposes an Aitken-based stochastic gradient algorithm for ARX models with time delay. By using the redundant rule, the ARX model can be transformed into an augmented model. Based on the Aitken method, the parameters of the augmented model can be estimated, and then, the unknown parameters of the ARX model and the time delay can be computed. The performance of the Aitken-based stochastic gradient algorithm is then analyzed. Furthermore, a numerical example and a real system example are provided to show the effectiveness of the proposed algorithm. Compared with the traditional stochastic gradient algorithm, the Aitken-based stochastic gradient algorithm achieves better convergence performance that the parameter estimation errors converge below 3% in both examples after 400 steps.

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Acknowledgements

This work is supported by the Joint Funds of the National Natural Science Foundation of China (No. U1734210), the National Natural Science Foundation of China (Nos. 61403165, K61603156) and the Qinglan Project of Jiangsu Province.

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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, People’s Republic of China

    Cheng Wang

  2. National Engineering Research Center of Rail Transportation Operation and Control System, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Kaicheng Li

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  1. Cheng Wang
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  2. Kaicheng Li
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Correspondence to Cheng Wang.

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Wang, C., Li, K. Aitken-Based Stochastic Gradient Algorithm for ARX Models with Time Delay. Circuits Syst Signal Process 38, 2863–2876 (2019). https://doi.org/10.1007/s00034-018-0998-y

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