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Trajectory Control of Convergent Networks

Neural Processing Letters volume 8, pages 99–106 (1998)Cite this article

Abstract

We present a class of feedback control functions which increase the convergence rates of nonlinear dynamical systems. A simple sign function is used to obtain convergence in finite time. We describe a trajectory learning procedure which preserves the convergence property of the system. Based on the proposed feedback, we developed a new neural network model which converges in finite time.

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References

  1. H.D. Chiang and J.S. Thorp, “Stability regions of nonlinear dynamical systems: A constructive methodology”, IEEE Transactions on Automatic Control, Vol. 34, No. 12, pp. 1229–1241, 1989.

    Google Scholar 

  2. M.A. Cohen, “The construction of arbitrary stable dynamics in nonlinear neural networks”, Neural Networks, Vol. 5, pp. 83–103, 1992.

    Google Scholar 

  3. J.J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons”, Proc. Nath. Acad. Sci. USA, Vol. 81, pp. 3088–3092, 1984.

    Google Scholar 

  4. H.K. Khail, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, 1996.

    Google Scholar 

  5. B.A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: A survey”, IEEE Transactions on Neural Networks, Vol. 6, No. 5, pp. 1212–1228, 1995.

    Google Scholar 

  6. N.B. Toomarian and J. Barhen, “Learning a trajectory using adjoint functions and teacher forcing”, Neural Networks, Vol. 5, pp. 473–484, 1992.

    Google Scholar 

  7. M. Zak, “Terminal attractors in neural networks”, Neural Networks, Vol. 2, pp. 259–274, 1989.

    Google Scholar 

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Authors and Affiliations

  1. Oak Ridge National Lab, P.O. Box 2008, Oak Ridge, TN, 37831-6355. E-mail: Email

    N. Peterfreund

  2. Department of Computer Science, Technion, Israel Institute of Technology, Haifa o[32000, Israel. Tel(USA)

    Y. Baram

Authors
  1. N. Peterfreund
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  2. Y. Baram
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Peterfreund, N., Baram, Y. Trajectory Control of Convergent Networks. Neural Processing Letters 8, 99–106 (1998). https://doi.org/10.1023/A:1009690109549

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  • DOI: https://doi.org/10.1023/A:1009690109549

  • dynamical neural networks
  • feedback control
  • finite time convergence
  • Lasalle theorem
  • learning
  • trajectory control