IJPAM: Volume 66, No. 4 (2011)


H.T. Banks$^1$, Taesoo Jang$^2$, Hee-Dae Kwon$^3$
$^1$Center for Research in Scientific Computation
Center for Quantitative Sciences in Biomedicine
North Carolina State University
Raleigh, NC, 27695-8212, USA
e-mail: [email protected]
$^{2,3}$Department of Mathematics
Inha University
Yonghyundong, Namgu, Incheon, 402-751, KOREA
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]

Abstract.In this presentation we apply a receding horizon observer to an HIV feedback control problem in order to derive optimal treatments of HIV progression and/or optimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. We use a nonlinear differential equation model which has been well-validated with clinical patient data and shown to have reliable predictive capabilities. The basic feedback control problem utilizes a tracking formulation (desired states for viral load and immune effector calculated from a healthy steady state for the model are tracked). Here we assume only very realistic observerables of $CD4+$ T cell count and viral load. Moreover, we use a second deterministic optimal tracking problem for state estimation as opposed to stochastic filtering approaches. In both of the optimization problems (for optimal feedback control and for state estimator) conjugate gradient algorithms are employed.

Received: January 5, 2011

AMS Subject Classification: 92C50, 92C42, 49K15, 93C10, 93C15

Key Words and Phrases: HIV, feedback control, receding horizon control, optimality systems and computational methods, state estimator, optimal tracking

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 4