Skip to main content
Log in

On the existence of overtaking trajectories

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

Abstract

A study is made of the conditions sufficient for the existence of overtaking trajectories for a class of infinite time-horizon, time-variant optimal control systems. Nonautonomy is restricted to disturbances with limits at infinity. The convergence property of the overtaking trajectories to the optimal steady-state limit is shown.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Haurie, A.,Optimal Control on an Infinite-Time Horizon: The Turnpike Approach, Journal of Mathematical Economics, Vol. 3, pp. 81–102, 1976.

    Google Scholar 

  2. Brock, W. A., andHaurie, A.,On Existence of Overtaking Optimal Trajectories over an Infinite-Time Horizon, Mathematics of Operations Research, Vol. 1, pp. 337–346, 1976.

    Google Scholar 

  3. Haurie, A.,Existence and Global Asymptotic Stability of Optimal Trajectories for a Class of Infinite-Horizon, Nonconvex Systems, Journal of Optimization Theory and Applications, Vol. 31, pp. 515–533, 1980.

    Google Scholar 

  4. Varaiya, P. P.,On the Trajectories of a Differential System, Mathematical Theory of Control, Edited by A. V. Balakrishnan and L. Neustadt, Academic Press, New York, New York, 1967.

    Google Scholar 

  5. Yano, M.,A Note on the Existence of an Optimal Capital Accumulation in the Continuous Time Horizon, Journal of Economic Theory, Vol. 27, pp. 421–429, 1982.

    Google Scholar 

  6. May, R. M., Beddington, J. R., Clark, C. W., Holt, S. J., andLaws, R. M.,Management of Multispecies Fisheries, Science, Vol. 205, pp. 267–277, 1979.

    Google Scholar 

  7. Haurie, A., andLeitmann, G.,On the Global Asymptotic Stability of Equilibrium Solutions for Open-loop Differential Games, Large Scale Systems, Vol. 6, pp. 107–122, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by P. Varaiya

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eirola, T., Kaitala, V. On the existence of overtaking trajectories. J Optim Theory Appl 49, 227–237 (1986). https://doi.org/10.1007/BF00940758

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00940758

Key Words

Navigation