Nonlinear Dynamics

, Volume 70, Issue 2, pp 1051–1059 | Cite as

Design of a fast convergent backpropagation algorithm based on optimal control theory

  • Mostafa Jahangir
  • Mehdi Golshan
  • Siavash Khosravi
  • Hossein Afkhami
Original Paper


The main contribution of this paper is using optimal control theory for improving the convergence rate of backpropagation algorithm. In the proposed approach, the learning algorithm of backpropagation is modeled as a minimum time control problem in which the step-size of its learning factor is considered as the input of this model. In contrast to the traditional backpropagation, learning algorithms which select the step-size by trial and error, it is selected adaptively based on optimal control criterion. The effectiveness of the proposed algorithm is evaluated in two simulations: XOR and 3-bit parity. In both simulation examples, the proposed algorithm outperforms well in speed and the ability to escape from local minima.


Backpropagation Neural network Optimal control Learning factor 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Mostafa Jahangir
    • 1
  • Mehdi Golshan
    • 1
  • Siavash Khosravi
    • 1
  • Hossein Afkhami
    • 2
  1. 1.Young Researchers Club, Sepidan BranchIslamic Azad UniversitySepidanIran
  2. 2.Department of Electronics, Sepidan BranchIslamic Azad UniversitySepidanIran

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