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Journal of Control Science and Engineering
Volume 2016, Article ID 6284574, 6 pages
http://dx.doi.org/10.1155/2016/6284574
Research Article

Nonlinear and Robust Control Strategy Based on Chemotherapy to Minimize the HIV Concentration in Blood Plasma

1Department of Biotechnology and Bioengineering, CINVESTAV-IPN, Avenida Instituto Politécnico Nacional 2508, 07360 San Pedro Zacatenco, DF, Mexico
2Facultad de Ciencias Química, Universidad Autónoma de San Luis Potosí, Álvaro Obregón No. 64, Colonia Centro, 78000 San Luis Potosí, SLP, Mexico
3División de Matemáticas Aplicadas, IPICYT, Camino a la Presa San José 2055, Colonia Lomas 4 Sección, 78216 San Luis Potosí, SLP, Mexico

Received 23 November 2015; Revised 13 April 2016; Accepted 26 April 2016

Academic Editor: Ai-Guo Wu

Copyright © 2016 Ricardo Aguilar-López et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A nonlinear PI-type control strategy is designed in order to minimize the HIV concentration in blood plasma, via medical drug injection, under the framework of bounded uncertain input disturbances. For control design it is considered a simplified mathematical model of the virus infection as a benchmark. The model is based on mass balances of healthy cells, infected cells, and the virus concentrations. The proposed controller contains a nonlinear feedback PI structure of bounded functions of the regulation error. The closed-loop stability of the system is analyzed via Lyapunov technique, in which robustness against system disturbances is demonstrated. Numerical experiments show a satisfactory performance of the proposed methodology as a HIV therapy, in which the virion particles and the infected CD4+T cells are minimized and, as an interesting result, the drug dosage can be suspended, thus avoiding drug resistance from the virus. Finally, the proposed controller is compared to a standard sliding-mode and hyperbolic tangent controllers showing better performance.