Skip to main content

Zhang Neural Network Versus Gradient Neural Network for Online Time-Varying Quadratic Function Minimization

  • Conference paper
Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence (ICIC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5227))

Included in the following conference series:

Abstract

With the proved efficacy on solving linear time-varying matrix or vector equations, Zhang neural network (ZNN) could be generalized and developed for the online minimization of time-varying quadratic functions. The minimum of a time-varying quadratic function can be reached exactly and rapidly by using Zhang neural network, as compared with conventional gradient-based neural networks (GNN). Computer-simulation results substantiate further that ZNN models are superior to GNN models in the context of online time-varying quadratic function minimization.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Leithead, W.E., Zhang, Y.: O(N 2)-Operation Approximation of Covariance Matrix Inverse in Gaussian Process Regression Based on Quasi-Netwon BFGS Method. Communications in Statistics – Simulation and Computation 36, 367–380 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Tsiotras, P., Corless, M., Rotea, M.: Optimal Control of Rigid Body Angular Velocity with Quadratic Cost. Journal of Optimization Theory and Applications 96, 507–532 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Zhang, Y.: Towards Piecewise-Linear Primal Neural Networks for Optimization and Redundant Robotics. In: Proceedings of IEEE International Conference on Networking, Sensing and Control, pp. 374–379. IEEE Press, Ft. Lauderdale (2006)

    Chapter  Google Scholar 

  4. Davey, K., Ward, M.J.: A Successive Preconditioned Conjugate Gradient Method for the Minimization of Quadratic and Nonlinear Functions. Applied Numerical Mathematics 35, 129–156 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gomez, M.A.: An O(n 2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs. Numerical Algorithms 27, 367–375 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Zhang, Y., Leithead, W.E., Leith, D.J.: Time-Series Gaussian Process Regression Based on Toeplitz Computation of O(N 2) Operations and O(N)-Level Storage. In: Proceedings of the 44th IEEE Conference on Decision and Control, pp. 3711–3716. IEEE Press, Sevilla (2005)

    Chapter  Google Scholar 

  7. Zhang, Y., Wang, J., Xia, Y.: A Dual Neural Network for Redundancy Resolution of Kinematically Redundant Manipulators Subject to Joint Limits and Joint Velocity Limits. IEEE Transactions on Neural Networks 14, 658–667 (2003)

    Article  Google Scholar 

  8. Mead, C.: Analog VLSI and Neural Systems. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  9. Manherz, R.K., Jordan, B.W., Hakimi, S.L.: Analog Methods for Computation of the Generalized Inverse. IEEE Transactions on Automatic Control 13, 582–585 (1968)

    Article  Google Scholar 

  10. Sturges Jr., R.H.: Analog Matrix Inversion (Robot Kinematics). IEEE Journal of Robotics and Automation 4, 157–162 (1988)

    Article  Google Scholar 

  11. Zhang, Y., Chen, K.: Global Exponential Convergence and Stability of Wang Neural Network for Solving Online Linear Equations. Electronics Letters 44, 145–146 (2008)

    Article  Google Scholar 

  12. Zhang, Y., Jiang, D., Wang, J.: A Recurrent Neural Network for Solving Sylvester Equation with Time-Varying Coefficients. IEEE Transactions on Neural Networks 13, 1053–1063 (2002)

    Article  Google Scholar 

  13. Zhang, Y., Ge, S.S.: Design and Analysis of a General Recurrent Neural Network Model for Time-Varying Matrix Inversion. IEEE Transactions on Neural Networks 16, 1477–1490 (2005)

    Article  Google Scholar 

  14. Zhang, Y.: Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion. In: Proceedings of IEEE International Symposium on Intelligent Control, pp. 1411–1416. IEEE Press, Limassol (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

De-Shuang Huang Donald C. Wunsch II Daniel S. Levine Kang-Hyun Jo

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, Y., Li, Z., Yi, C., Chen, K. (2008). Zhang Neural Network Versus Gradient Neural Network for Online Time-Varying Quadratic Function Minimization. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2008. Lecture Notes in Computer Science(), vol 5227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85984-0_97

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85984-0_97

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85983-3

  • Online ISBN: 978-3-540-85984-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics