Hyeygjeon Chang

Control of HIV Infection Dynamics

This article describes a drug scheduling method based on a reduced-order model, which does not require estimates of all of the parameters and states of the full-order model. To this end, we divide the full-order model into two subsystems, one of which is modified to approximate the full-order model. We show that the suggested method drives the HIV patient state into the LTNP region of attraction. This article is organized as follows. First, the problem under consideration is formulated, and a description of the HIV infection model is provided. Then, measurement methods for the states of the HIV model are surveyed. Subsequently the HIV infection model is modified to yield a reduced-order model. Finally, two control strategies based on this modified model are presented along with simulation results. The article concludes with a discussion and ideas for future work.

Brief paper: Enhancement of the immune system in HIV dynamics by output feedback

The human immunodeficiency virus infection, that causes acquired immune deficiency syndrome, is a dynamic process that can be modeled via differential equations. In this paper we introduce an output feedback method designed for antiretroviral drug therapy to control the immune response. The purpose of the method is to steer the system to an equilibrium condition, the long-term nonprogressor, which corresponds to an infected patient who does not develop the symptoms of acquired immune deficiency syndrome. The suggested control idea guarantees that the immune state is enhanced to a certain level, which is enough for a typical patient to be driven into the long-term nonprogressor status.

A system theoretic study on a treatment of AIDS patient by achieving long-term non-progressor

There has been much recent interest in the long-term non-progressor (LTNP), who has been infected with human immunodeficiency virus (HIV) but does not proceed to AIDS. Under the assumption that a mathematical model describing the HIV infection and drug effects is true for real systems, we claim that it is possible to steer the state of any patients to that of LTNP if the model parameters belong to the proposed parameter intervals. Once the state is transferred close to LTNP, CTL memory is established and the viral load remains very low level even after the medication is stopped. In order to justify the claim, we first analyze the stability and the bifurcation of the model and show that there exists an equilibria curve towards LTNP, which is stable for all fixed constant inputs except some singular points. Then, we propose a new treatment strategy based on a useful property of Non-vanishing Basin of Attraction (NvBA)-stability. An extensive simulation study is also included to validate the proposed treatment for various initial conditions and to show the robustness against the parameter uncertainty. From a practical perspective, it deserves further investigation whether the proposed treatment strategy could switch a patient into LTNP in the real world.

Activation of Immune Response in Disease Dynamics via Controlled Drug Scheduling

The human immunodeficiency virus (HIV) infection, that causes acquired immune deficiency syndrome (AIDS), is a dynamic process that can be modeled via differential equations. The primary goal of this paper is to introduce a control philosophy to boost the response of the immune system by means of drug scheduling. The control purpose is to steer the system to an equilibrium condition known as long-term nonprogressor, which corresponds to an infected patient that does not develop the symptoms of AIDS. The feasibility of the control methodology is illustrated via simulations on two HIV dynamic models and on a general disease model.

Immune response’s enhancement via controlled drug scheduling

The human immunodeficiency virus (HIV) infection, that causes acquired immune deficiency syndrome (AIDS), is a dynamic process that can be modeled via differential equations. The primary goal of this paper is to introduce a control philosophy to boost the response of the immune system by means of drug scheduling. The control goal is to steer the system to an equilibrium condition, known as nonprogressor, which corresponds to an infected patient that does not develop the symptoms of AIDS. The feasibility of the control methodology is illustrated via simulations on two HIV dynamic models and on a general disease model.

Non-vanishing basin of attraction with respect to a parametric variation and center manifold

When the origin of a nonlinear system having a parameter is locally asymptotically stable, the size of its basin of attraction may also depend on the parameter. If the parameter variation is confined within a compact interval and if the origin is locally exponentially stable for each parameter, then it is well-known that the radius of basin of attraction does not shrink to zero under the variation of parameter. We relax this condition up to the case where the origin loses exponential stability for a certain parameter. This is done by focusing on the behavior of the system on a parametrized center manifold. In addition, by introducing the concept of stability with respect to a positively invariant subset of the state-space, the proposed analysis is applicable to the case where the system experiences bifurcation of splitting or merging equilibria, which often appears in biological systems. The stability property considered here is called for with the boundary layer system in the singular perturbation context, or with the system having slowly varying inputs. The main results establish that the non-vanishing basin of attraction (relative to a positively invariant set) is guaranteed by confirming the similar property just for the reduced order system on a parametrized center manifold.

Estimation of immune states in HIV dynamics

The human immunodeficiency virus infection, that causes acquired immune deficiency syndrome, is a dynamic process that can be modeled via differential equations. In the literature of control applications, model-based control methods to boost the immune system by means of drug scheduling have been reported. The control purpose is to steer the system to an equilibrium condition, known as long-term nonprogressor, which corresponds to an infected patient that does not develop the symptoms of acquired immune deficiency syndrome. In this paper we investigate methods to estimate the state of the immune system based on the available outputs of the HIV model. A nonlinear observer is designed and an approximate observer is also given. Computer simulations are presented to show the feasibility of the estimation methodology.

Enhancement of the immune response to chronic myeloid leukaemia via controlled treatment scheduling

We study the differential equations describing the chronic myeloid leukaemia. We propose a novel drug scheduling method to enhance the T-cell mediated immune response. The control strategy relies on the understanding of the immune boosting mechanism. The feasibility of the strategy is illustrated via simulations.

Control of the HIV Infection Dynamics with a Reduced Second Order Model

The HIV infection is a dynamic process that can be modeled mathematically. By means of changing the drug effect in the model, the primary goal of this paper is to show how to drive any initial state into an equilibrium called the nonprogressor, where the infected patient does not develop symptoms of AIDS. The goal is achieved by a new method of treatment. This method is based on an approximation of higher order dynamics by a reduced order model. For the approximation, we divide the HIV infection model into two subsystems and modify one of the subsystems to emulate the whole system. With the modification, we relieve the load to deal with the high order model, such as state observation and parameter estimation. The effectiveness of the new treatment is demonstrated by computer simulations.

Robust multi-parametric model predictive control for discrete-time LPV systems

In this paper we study mpMPC problem for discrete-time, linear parameter varying systems exploiting the solution of the mpMPC for linear time invariant (LTI) systems. The proposed control method yields a controller which is adapted to take parameter changes into account. Thus it could improve the performance of mpMPC in terms of robustness to the presence of slowly varying parameters. It is expected that the method can be applied to process systems which suffer from slow variation of system parameters, such as aging and degradation. The proposed control method can be implemented conveniently as an add-on to the current mpMPC without any modification of the established mpMPC algorithm for LTI systems. Also the method consists of simple computational steps thus can be run on-line.