Observer-Based Impulsive Controller Design for Treatment of Hepatitis C Disease

In this study, an impulsive state feedback controller has been proposed for the treatment of hepatitis-C-infected patients under Pegylated-Interferon (PEG-IFN-α2b) therapy. The Neumann model has been utilized as the representative of the hepatitis C virus (HCV) dynamics. In order to consider the drug efficacy variation between injections, the pharmacokinetics/pharmacodynamics (PK/PD) equations have been included in the model. The impulsive nature of the drug injection also has been considered in the disease dynamics. In the proposed treatment method, the drug dose limitation has been addressed as an input nonlinearity. The asymptotical stability of the control method under the impulsive nature of the drug administration and its limited dose amount have been shown through the use of a combination of a heuristic approach and the Lyapunov theory. For the implementation of the control strategy, all system states should be available, while only the viral load is measured at certain discrete times. In order to solve this problem, a nonlinear impulsive Luenberger-like observer has been designed to estimate the unknown states. Finally, the effectiveness of the controller under impulsive and limited input with and without the observer has been investigated via simulation study. The results show that, in both cases, the treatment objective has been achieved and the viral load decreases to its desired value. The observer also has good performance, and the estimated states converge to their actual values.