Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T08:06:21.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal control on an infinite domain

Published online by Cambridge University Press:  17 February 2009

B. D. Craven
B. D. Craven
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For an optimal control problem with an infinite time horizon, assuming various terminal state conditions (or none), terminal conditions for the costate are obtained when the state and costate tend to limits with a suitable convergence rate. Under similar hypotheses, the sensitivity of the optimum to small perturbations is analysed, and in particular the stability of the optimum when the infinite horizon is truncated to a large finite horizon. An infinite horizon version of Pontryagin's principle is also obtained. The results apply to various economic models.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 2 , October 2005 , pp. 143 - 153
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Chiang, A. C., Elements of dynamic optimization (Waveland Press, Prospect Heights, Illinois, 2000).Google Scholar
[2]Craven, B. D., Control and optimization (Chapman and Hall, London, 1995).CrossRefGoogle Scholar
[3]Craven, B. D. and Islam, S. M. N., Optimization in economics and finance: some advances in non-linear, dynamic, multi-criteria and stochastic models (Springer, Amsterdam, 2005).Google Scholar
[4]Janin, R., “Conditions nécessaires d'optimalité dans un problème d'optimisation en horizon infini”, C. R. Acad. Sci. Paris 289A (1979) 651–653.Google Scholar
[5]Leonard, D. and Long, N. V., Optimal control theory and static optimization in economics (Cambridge University Press, Cambridge, UK, 1992).Google Scholar
[6]Michel, P., “On the transversality conditions in infinite horizon optimal problems”, Econometrica 50 (1982) 975–985.CrossRefGoogle Scholar
[7]Ramsey, F., “A mathematical theory of saving”, Economic J. 38 (1928) 543–559.Google Scholar