Volume 2, Issue 1, January 2017, Page: 6-13
Applications of B-transform to Some Impulsive Control Problems
Benjamin Oyediran Oyelami, Department of Mathematics, Plateau State University, Bokkos, Nigeria
Received: Sep. 4, 2016;       Accepted: Jan. 17, 2017;       Published: Feb. 21, 2017
DOI: 10.11648/j.mcs.20170201.12      View  3868      Downloads  140
In this paper, B-transform is applied to some impulsive control models and closed solution forms for the models obtained. The problems solved via the B-transform are the third order linear impulsive control systems with bang-bang control, Impulsive delay control systems, Impulsive heat control systems, the Impulsive diffusion problem and the impulsive Gross berg control model. Simulation for the bang bang model show that the solutions are negative and positive in some for given time interval. The solutions also exhibit non-periodic and non-oscillatory behaviour in the given interval. The solutions of impulsive diffusion model possess singularities in given interval of simulation.
Impulsive, Control Systems, Bang-Bang, B-transform
To cite this article
Benjamin Oyediran Oyelami, Applications of B-transform to Some Impulsive Control Problems, Mathematics and Computer Science. Vol. 2, No. 1, 2017, pp. 6-13. doi: 10.11648/j.mcs.20170201.12
Copyright © 2017 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.
A. El-Ajou, O. Abu Arqub, S. Momani, Approximate analytical solution of the nonlinear fractional KdV Burgers equation: A new iterative algorithm, Journal of Computational Physics 293 (2015) 81-95
Abu Arqub O., B. Maayah, Solutions of Bagley-Torvik and Painlevé equations of fractional order using iterative reproducing kernel algorithm, Neural Computing & Applications, 2016. DOI 10.1007/s00521-016-2484-4.
Ale S. O. and Oyelami, B. O.: Impulsive System and Applications, Int. J. Math. Edu. Sci. Technol., 2000 Vol., 31, No. 4, 539-544.
Ale S O. and Oyelami B. O. B-Stability and its applications to some constant delay impulsive control models. NMC-COMSATS Proceedings on International Conference on Mathematical Modelling of some Global Challenges in the 21st Century, 2009, pp56-65. http://nmcabuja.org/nmc_proceeding.html.
Bainov, D. D., Lakshikantham, V. and Simeonov, P. S.: Theory of Impulsive Differential Equations (Singapore; World Scientific Publication), 1989.
Hong Shi, Guangming Xie, Controllability and observability criteria for linear piecewise constant impulsive systems, J. Applied Maths. (2012).
Oyelami, B. O. and Ale, S. O.: B-transform method and its applications, in obtaining solutions of some impulsive models. Int. J. Math. Edu. Sc. Tech., 2000, Vol. 31, No. 4, 525-538.
Oyelami, B. O., Ale, S. O., Onumanyi P., Ogidi J. A.: B-transform method and application to sickle cell aneamia. Proc. International Seminar on Theoretical Physics and National Development. Published in a special issue of the African Journal of Physics, 2008, Pp202-220. http://sirius-c.ncat.edu/asn/ajp/allissue/ajp-ISOTPAND/index.html
Oyelami B O and Ale S O. Impulsive differential equations and applications to some models: Theory and applications. A monograph, Lambert Academic Publisher Germany, March 24, 2012. ISBN: 978-3-8484-4740-4.
Oyelami, B. O. and Ale, S. O.: B-transform and its applications to a fish-hyacinth model, Int. J. Math. Educ. Sci. Techno 2002 Vol. 33, No. 4, 565 - 573.
Oyelami, B. O., Ale, S. O., Onumanyi P., Ogidi J. A.: Impulsive HIV-1 model in the presence of antiretroviral drugs using B-transform method. Proc. African Mathematical Union, 2003, 62-76. Oyelami, B. O., Ale, S. O., Onumanyi P.:
Impulsive HIV model using B-transform. Proceedings of National Mathematical Centre on Conference on Computational Mathematics. Vol.2, No.1, 2005, pp50-64. http://nmcabuja.org/nmc_proceedings.html; http://math.golonka.se/nmc_proceeding.
Oyelami B O and Ale S O. Impulsive model for the absorption of oxygen by the red blood cells in the presence of nitric oxide yielding drugs. African Journal of Physics, Vol.3, 2010. http://sirius-c.ncat.edu/asn/afps/ajp/ajp-ISOTPAND10/Proc%20ISPD%20book145-163.pdf
Oyelami B O and Ale S O. Solutions of Impulsive Diffusion and Von-Foerster Makendrick models using the B-transform. Applied Mathematics Journal, 2013, 4, 1637-1646. (http://www.scirp.org/journal/am) http:/dx.doi.org/10.4236/am.2013.412223.
Oyelami B O. δ-Controllability of impulsive systems and application to some physical and biological control systems. International Journal of Differential Equations and Applications.vol.12, no.3, 2013. http:/dx.doi.org/10.12732/ijdea.v12i3.1093. www.ijpam.eu/en/index.php/idea/article/view/1093/0
Simeonov, P. S. and Bainov, D. D.; Theory of impulsive differential equations: periodic solutions and applications. Longman, Essex, 1993.
Wen C. Y., Li Z. G., Soh Y. C., Analysis and design of impulsive control system, IEEE Transaction on Automatic Control, 46, No. 6 (2001).
Zhi-Hong Guan, J. David Hill, Xuemin (Sherman) Shen, on hybrid impulsive and switching systems and applications to nonlinear control. IEEE Transaction on Automatic Control, 50, No. 7 (2005).pp 1058-1062.
Saker S. H., Alzabut J. O., on the impulsive delay haematopoiesis model with periodic coefficients, Rocky Mountain J. Math., 39, No. 5 (2009), 1657-1688.
Browse journals by subject