Skip to main content
SpringerLink
Log in

Convergence of a feasible directions algorithm for relaxed controls in time-lag systems

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, we consider a class of time-lag optimal control problems involving control and terminal inequality constraints. A feasible direction algorithm has been obtained by Teo, Wong, and Clements for solving this class of optimal control problems. It was shown that anyL ∞ accumulation points of the sequence of controls generated by the algorithm satisfy a necessary condition for optimality. However, suchL ∞ accumulation points need not exist. The aim of this paper is to prove a convergence result, which ensures that the sequence of controls generated by the algorithm always has accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed problem.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Teo, K. L., Wong, K. H., andClements, D. J.,A Feasible Directions Algorithm for Time-Lag Optimal Control Problems with Control and Terminal Inequality Constraints, Journal of Optimization Theory and Applications, Vol. 46, pp. 295–317, 1985.

    Google Scholar 

  2. Polak, E., andMayne, D. Q.,A Feasible Directions Algorithm for Optimal Control Problems with Control and Terminal Inequality Constraints, IEEE Transactions on Automatic Control, Vol. AC-22, pp. 741–751, 1977.

    Google Scholar 

  3. Teo, K. L., andWu, Z. S.,Computational Methods for Optimizing Distributed Systems, Academic Press, New York, New York, 1984.

    Google Scholar 

  4. Williamson, L. J., andPolak, E.,Relaxed Controls and the Convergence of Algorithms, SIAM Journal on Control and Optimization, Vol. 14, pp. 737–756, 1976.

    Google Scholar 

  5. Teo, K. L.,Convergence of a Conditional Gradient Algorithm for Relaxed Controls Involving First Boundary-Value Problems of Parabolic Type, Numerical Functional Analysis and Optimization, Vol. 6, pp. 457–491, 1983.

    Google Scholar 

  6. Teo, K. L., Clements, D. J., Wu, Z. S., andChoo, K. G.,Convergence of a Strong Variational Algorithm for Relaxed Controls Involving a Class of Hyperbolic Systems, Journal of Optimization Theory and Applications, Vol. 42, pp. 467–485, 1984.

    Google Scholar 

  7. Murray, J. M., andTeo, K. L.,On a Computational Algorithm for a Class of Optimal Control Problems Involving Discrete Time-Delayed Arguments, Journal of the Australian Mathematical Society, Series B, Vo. 20, pp. 315–343, 1978.

    Google Scholar 

  8. Wong, K. H., andTeo, K. L.,A Conditional Gradient Method for a Class of Time-Lag Optimal Control Problems, Journal of the Australian Mathematical Society, Series B, Vol. 25, pp. 518–537, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Kent Ridge, Singapore

    S. J. Wilson (Associate Professor)

  2. Department of Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa

    K. H. Wong (Lecturer)

Authors
  1. S. J. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. H. Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by E. Polak

This work was done when the first author was on sabbatical leave at the School of Mathematics, University of New South Wales, Australia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wilson, S.J., Wong, K.H. Convergence of a feasible directions algorithm for relaxed controls in time-lag systems. J Optim Theory Appl 53, 461–474 (1987). https://doi.org/10.1007/BF00938950

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00938950

Key Words

Search

Navigation