Improved gradient descent algorithms for time-delay rational state-space systems: intelligent search method and momentum method


This study proposes two improved gradient descent parameter estimation algorithms for rational state-space models with time-delay. These two algorithms, based on intelligent search method and momentum method, can simultaneously estimate the time-delay and parameters without the matrix eigenvalue calculation in each iteration. Compared with the traditional gradient descent algorithm, the improved algorithms come with two advantages: having quicker convergence rates and less computational efforts, particularly meaningful for those large-scale systems. A simulated example is selected to illustrate the efficiency of the proposed algorithms.

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The authors would like to thank the Associate Editor and the anonymous reviewers for their constructive and helpful comments and suggestions to improve the quality of this paper.


This study was funded by the National Natural Science Foundation of China (No. 61973137) and the Funds of the Science and Technology on Near-Surface Detection Laboratory (No. TCGZ2019A001).

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Correspondence to Jing Chen.

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This work is supported by the National Natural Science Foundation of China (No. 61973137) and the Funds of the Science and Technology on Near-Surface Detection Laboratory (No. TCGZ2019A001).

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Chen, J., Zhu, Q., Hu, M. et al. Improved gradient descent algorithms for time-delay rational state-space systems: intelligent search method and momentum method. Nonlinear Dyn (2020).

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  • Rational model
  • Time-delay
  • Gradient descent
  • Intelligent search method
  • Momentum method