Published

2008-05-01

Designing robust control-based HIV-treatment

Diseño de tratamientos para VIH basados en control robusto

Keywords:

robust control, polytopic system, HIV, AIDS, mathematical model, immune system dynamics (en)
control robusto, sistema politópico, VIH, sida, modelos matemáticos, dinámica del sistema inmune (es)

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Authors

  • Fredy Andrés Olarte Dussán Universidad Nacional de Colombia
  • Carlos Arturo Clavijo Ramírez Universidad Nacional de Colombia
  • Hernando Díaz Morales Universidad Nacional de Colombia
Designing a robust control-based treatment for human immunodeficiency virus (HIV)-infected patients was studied. The dynamics of the immune system’s response to infection was modelled using a 5th order nonlinear model with separate efficacy coefficients for protease inhibitor (PIs) and reverse transcriptase inhibitors (RTIs). The immune res-ponse has been represented as an uncertain system due to errors in parameter estimation and the existence of un-modelled dynamics. A polytopic system was constructed incorporating all possible system parameter values. A con-trol system was designed using robust pole location techniques stabilising the polytopic system around an equilibrium point having a low viral load. Numerical simulation results (including the organism’s pharmacokinetical response to anti-retroviral drugs) showed that the control law could lead to long-term stable conditions, even in extreme cases.
Este artículo describe el diseño de tratamientos para pacientes contagiados con virus de inmunodeficiencia humana (VIH), usando técnicas de control robusto. La dinámica de la respuesta del sistema inmune ante la infección se mo-dela por medio de un sistema no lineal de quinto orden, el cual incluye diferentes coeficientes de eficacia para el inhibidor de proteasa (PI) y el inhibidor de transcriptasa reversa (RTI). Debido a los inevitables errores en la estima-ción de parámetros y a la existencia de dinámicas no modeladas, la respuesta inmune se representa por medio de un sistema con incertidumbre: se construye un sistema politópico que incorpora todos los valores posibles de los parámetros del sistema. Se diseña un controlador para este sistema, usando técnicas robustas de localización de polos, para estabilizar el sistema politópico alrededor de un punto de equilibrio con carga viral muy pequeña. Los resultados simulados, incluyendo la respuesta farmacodinámica del organismo, muestran que la ley de control así diseñada conduce a una condición estable en el largo plazo, aun en casos extremos de variación de parámetros.

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Copyright (c) 2008 Fredy Andrés Olarte Dussán, Carlos Arturo Clavijo Ramírez, Hernando Díaz Morales

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