Volume 5, Issue 3, June 2016, Page: 77-81
Optimal Control and Hamiltonian System
Estomih Shedrack Massawe, Department of Mathematics, College of Natural Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania
Received: Apr. 16, 2016;       Accepted: Apr. 28, 2016;       Published: May 10, 2016
DOI: 10.11648/j.pamj.20160503.13      View  3332      Downloads  123
Abstract
In this paper, an optimal control for Hamiltonian control systems with external variables will be formulated and analysed. Necessary and sufficient conditions which lead to Pantryagin’s principle are stated and elaborated. Finally it is shown how the Pontryagin’s principle fits very well to the theory of Hamiltonian systems. The case of Potryagin’s maximum principle will be considered in detail since it is capable of dealing with both unbounded continuous controls and bounded controls which are possibly discontinuous.
Keywords
Optimal Control, Hamiltonian Systems, Conditions for Optimality
To cite this article
Estomih Shedrack Massawe, Optimal Control and Hamiltonian System, Pure and Applied Mathematics Journal. Vol. 5, No. 3, 2016, pp. 77-81. doi: 10.11648/j.pamj.20160503.13
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, Inc., 1975.
[2]
N. U. Ahmed, Optimal control of stochastic dynamical systems, Information and Control, Volume 22, Issue 1, pp. 13-30, 1973.
[3]
V. Radisavljevic and H. Baruh, Journal of Dynamic Systems, Measurement, and Control, 121(4), pp. 594-598, 1999.
[4]
S. Schaa1, P., Mohajerian1 and A. Ijspeert, Progress in Brain Research, Vol. 165, pp. 425-445, 2007.
[5]
S. Lafortune, Introduction to Discrete Event Systems, The International Series on Discrete Event Dynamic Systems, 1993.
[6]
M. H. Huller, K. Kunisch, Y. S., S. Volkwein, International Journal for Numerical Methods in Fluids, 00:1-6, 2000.
[7]
S. Barnet and R. G. Cameron R. G, Introduction to Mathematical Control Theory, Clarendon Press, 1985.
[8]
E. S. Massawe, Hamiltonian Control Systems, International Journal of Theoretical and Mathematical Physics 2016, 6(1): pp. 26-30.
[9]
V. der Schaft, System Theoretic Description of Physical System, Doctoral Thesis, Mathematical Centrum, Amsterdam, 1984.
[10]
E. S. Massawe, Hamiltonian Control Systems, Unpublished M.Sc Thesis, University of Dublin.
Browse journals by subject