Optimal Control and Hamiltonian System

Estomih Shedrack Massawe

doi:doi:10.11648/j.pamj.20160503.13

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Optimal Control and Hamiltonian System

Estomih Shedrack Massawe

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 3)

Received: 16 April 2016 Accepted: 28 April 2016 Published: 10 May 2016

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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.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 3)
DOI	10.11648/j.pamj.20160503.13
Page(s)	77-81
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Optimal Control, Hamiltonian Systems, Conditions for Optimality

References

[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.

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Estomih Shedrack Massawe. (2016). Optimal Control and Hamiltonian System. Pure and Applied Mathematics Journal, 5(3), 77-81. https://doi.org/10.11648/j.pamj.20160503.13

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ACS Style

Estomih Shedrack Massawe. Optimal Control and Hamiltonian System. Pure Appl. Math. J. 2016, 5(3), 77-81. doi: 10.11648/j.pamj.20160503.13

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AMA Style

Estomih Shedrack Massawe. Optimal Control and Hamiltonian System. Pure Appl Math J. 2016;5(3):77-81. doi: 10.11648/j.pamj.20160503.13

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@article{10.11648/j.pamj.20160503.13,
  author = {Estomih Shedrack Massawe},
  title = {Optimal Control and Hamiltonian System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {3},
  pages = {77-81},
  doi = {10.11648/j.pamj.20160503.13},
  url = {https://doi.org/10.11648/j.pamj.20160503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160503.13},
  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.},
 year = {2016}
}

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TY  - JOUR
T1  - Optimal Control and Hamiltonian System
AU  - Estomih Shedrack Massawe
Y1  - 2016/05/10
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160503.13
DO  - 10.11648/j.pamj.20160503.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 77
EP  - 81
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160503.13
AB  - 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.
VL  - 5
IS  - 3
ER  -

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Author Information

Estomih Shedrack Massawe

Department of Mathematics, College of Natural Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania

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Plain Text BibTeX RIS

APA Style

Estomih Shedrack Massawe. (2016). Optimal Control and Hamiltonian System. Pure and Applied Mathematics Journal, 5(3), 77-81. https://doi.org/10.11648/j.pamj.20160503.13

Copy | Download

ACS Style

Estomih Shedrack Massawe. Optimal Control and Hamiltonian System. Pure Appl. Math. J. 2016, 5(3), 77-81. doi: 10.11648/j.pamj.20160503.13

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AMA Style

Estomih Shedrack Massawe. Optimal Control and Hamiltonian System. Pure Appl Math J. 2016;5(3):77-81. doi: 10.11648/j.pamj.20160503.13

Copy | Download

@article{10.11648/j.pamj.20160503.13,
  author = {Estomih Shedrack Massawe},
  title = {Optimal Control and Hamiltonian System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {3},
  pages = {77-81},
  doi = {10.11648/j.pamj.20160503.13},
  url = {https://doi.org/10.11648/j.pamj.20160503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160503.13},
  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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Optimal Control and Hamiltonian System
AU  - Estomih Shedrack Massawe
Y1  - 2016/05/10
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160503.13
DO  - 10.11648/j.pamj.20160503.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 77
EP  - 81
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160503.13
AB  - 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.
VL  - 5
IS  - 3
ER  -

Copy | Download