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This paper presents an algorithm for nonlinear adaptive control of the viral load in HIV-1 infection. The infection model considered is a reduced complexity nonlinear state-space model with two state variables, that represent the plasma concentration of uninfected and infected CD4+ T-cells of the human immune system. The viral load is assumed to be proportional to the concentration of infected cells. First, a change of variables that exactly linearizes the system is obtained. For the resulting linear system the manipulated variable is obtained by state feedback. To compensate for the uncertainty in the infection parameter of the model an estimator based on a Control Lyapunov Function is designed.
A control design procedure is proposed for a large class of discrete-time non-linear systems which combines exact linearization by feedback techniques with an established linear controller design methodology. The combined system thus inherits many of the characteristics of the linear system with regard to tracking, disturbance rejection and robustness. The design both of the linearizing feedback and of the overall linear controller is analyzed and example systems are used to illustrate the design method and demonstrate the performance characteristics of the closed-loop system. Special consideration is given to the effect of the non-linear feedback components on the performance of the controlled system under disturbance conditions and in the case of model mismatch.
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