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Adaptive Observer for Estimating the Parameters of an HIV Model with Mutants

Authors
Kim, Seok-KyoonKim, DonghuYoon, Tae-Woong
Issue Date
2월-2015
Publisher
INST CONTROL ROBOTICS & SYSTEMS, KOREAN INST ELECTRICAL ENGINEERS
Keywords
Adaptive observer; bifurcation; HIV model; mutant dynamics; parameter estimation
Citation
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS, v.13, no.1, pp.126 - 137
Indexed
SCIE
SCOPUS
KCI
Journal Title
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
Volume
13
Number
1
Start Page
126
End Page
137
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/94493
DOI
10.1007/s12555-013-9018-y
ISSN
1598-6446
Abstract
Human immunodeficiency virus (HIV) causes acquired immune deficiency syndrome (AIDS). The process of infection and mutation by HIV can be described by fifth-order ordinary differential equations. These equations can be reduced to third-order differential equations through the singular perturbation theory. The objective of this paper is to present a parameter estimation algorithm for this third-order HIV model, using two (out of three) state variables. We first show that the parameters of the HIV model are identifiable with these measurements. The structure of the proposed estimator parallels that of the full state feedback estimator with the unavailable state replaced with an estimated variable. We then prove that the resulting adaptive observer equipped with the so-called sigma-modification can be tuned to be ultimately bounded under some conditions in terms of the concentration of uninfected CD4+ T cells. Furthermore, it is seen through computer simulations that an iterative application of the proposed algorithm is effective; the estimated parameters approach their true values, and the stability analysis of the ensuing HIV model leads to the results that are consistent with those obtained previously.
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