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Fractional order system identification using a joint multi-innovation fractional gradient descent algorithm.

Zishuo Wang1, Beichen Chen1,2, Hongliang Sun1

  • 1School of Information and Control Engineering, Jilin Institute of Chemical Technology, Jilin, 132022, China.

Scientific Reports
|December 27, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a novel joint multi-innovation fractional gradient descent algorithm for identifying fractional order systems. The method enhances accuracy by simultaneously estimating system parameters and fractional orders, validated by simulations and real-world experiments.

Keywords:
Convergence analysisFractional order systemIdentificationJoint fractional gradient descentMulti-innovation theory

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Area of Science:

  • Control Systems Engineering
  • Applied Mathematics
  • Signal Processing

Background:

  • Fractional order systems offer enhanced modeling capabilities compared to integer order systems.
  • Accurate identification of both parameters and orders is crucial for effective control and analysis of these systems.
  • Existing identification algorithms may face challenges in simultaneously estimating parameters and orders efficiently.

Purpose of the Study:

  • To develop a novel joint multi-innovation fractional gradient descent algorithm for fractional order system identification.
  • To improve the accuracy and robustness of parameter and order estimation in fractional order systems.
  • To theoretically analyze the convergence properties of the proposed algorithm.

Main Methods:

  • Leveraging fractional calculus to design a joint fractional gradient descent algorithm for simultaneous parameter and order estimation.
  • Utilizing estimated parameters as initial conditions for order identification and vice-versa for iterative refinement.
  • Incorporating multi-innovation theory to enhance the convergence speed and identification accuracy of the gradient descent approach.

Main Results:

  • The proposed joint multi-innovation fractional gradient descent algorithm effectively estimates both parameters and orders of fractional order systems.
  • The algorithm demonstrates improved system identification accuracy compared to standard methods.
  • Theoretical convergence analysis confirms the stability and reliability of the proposed identification technique.

Conclusions:

  • The developed algorithm provides an effective solution for the identification of fractional order systems.
  • Numerical simulations and experimental validation on a flexible linkage system confirm the algorithm's practical applicability and effectiveness.
  • The joint iterative approach and multi-innovation strategy significantly enhance identification performance.