Skip to main content

Computation of Feedback Control for Infinite Time Optimal Control Problems

  • Chapter

Part of the book series: Applied Optimization ((APOP,volume 52))

Abstract

In this paper, we use an interactive multivariate interpolation method proposed by T.A. Foley and G.M. Nielson in conjuction with a cardinal product spline approach to compute a suboptimal feedback controller for a class of infinite time optimal control problems. Two examples have been solved to illustrate the efficiency of the method.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ahmed, N.U. (1988), Elements of Finite-Dimensional Systems and Control Theory, Pitman Monographs and Surveys in Pure and Applied Mathematics 37, Longman Sciences and Technical.

    MATH  Google Scholar 

  • Bryson, A.E., and Ho, Y.C. (1978), Applied Optimal Control, Hemisphere Publishing Corporation.

    Google Scholar 

  • Edwards, N. (1991), Synthesising Optimal Feedback Control with Neural Networks, Honours disertation, The University of Western Australia.

    Google Scholar 

  • Foley, T.A. (1979), Smooth Multivariate Interpolation to Scattered Data, Ph.D. dissertation, Arizona State University.

    Google Scholar 

  • Foley, T.A., and Nielson, G.M. (1980), Multivariate Interpolation to Scattered Data Using Delta Iteration, Approximation Theory III.

    Google Scholar 

  • Jennings, L.S., Fisher, M.E., Teo, K.L., and Goh, C.J. (1990), MISERS Optimal Control Software: Theory and User Manual, EMCOSS Pty Ltd.

    Google Scholar 

  • Lee, H.W.J., Teo, K.L., and Rehbock, V. (1995), Sub-optimal local feedback control for a class of nonlinear control problems, Dynamics of Continuous, Discrete and impulsive Systems, Vol. 1, pp. 37–51.

    MathSciNet  MATH  Google Scholar 

  • Narendra, K.S., and Parthasarathy, K. (1990), Identification and control of dynamical systems using neural networks, IEEEE Trans. on Neural Networks, Vol. 1, No. 1.

    Google Scholar 

  • Rehbock, V., Teo, K.L., and Jennings, L.S. (1995), Suboptimal feedback control for a class of nonlinear systems using Ssline interpolation, Discrete and Continuous Dynamical Systems, Vol. 1, No. 2.

    Google Scholar 

  • Shepard, D. (1968), A two-dimensional interpolation function for irregularly-spaced data, Proceedings 23rd ACM National Conference.

    Google Scholar 

  • Sirisena, H.R., and Chou, F.S. (1979), convergence of the control parameterization Ritz method for nonlinear optimal control problems, Journal of Optimization Theory and Applications, Vol. 29, pp. 369–382.

    Article  MathSciNet  MATH  Google Scholar 

  • Teo, K.L., Fisher, M.E., and Moore, J.B. (1993), A suboptimal feedback stabilizing controller for a class of nonlinear regulator problems, Applied Mathematics and Computation, Vol. 59, pp. 1–17.

    Article  MathSciNet  MATH  Google Scholar 

  • Teo, K.L., Goh, C.J., and Wong, K.H. (1991) A Unified Computational Approach to Optimal Control Problems, Longman Sciences and Technical.

    MATH  Google Scholar 

  • Teo, K.L., Wong, K.H., and Yan, W.Y. (1995), Gradient-flow approach for computing a nonlinear-quadratic optimal-output feedback gain matrix, Journal of Optimization Theory and Applications, Vol. 85, No. 1 pp. 75–96.

    Article  MathSciNet  MATH  Google Scholar 

  • Wong, K.H. (1988), A control parameterization algorithm for nonlinear time-lag optimal control problems, Journal of the Operation Research Society of India, Vol 25, No. 3, pp. 177–184.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Wong, K.H., Peter, G. (2001). Computation of Feedback Control for Infinite Time Optimal Control Problems. In: Yang, X., Teo, K.L., Caccetta, L. (eds) Optimization Methods and Applications. Applied Optimization, vol 52. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3333-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3333-4_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4850-2

  • Online ISBN: 978-1-4757-3333-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics