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

Abstract

In this study, an impulsive state feedback controller has been proposed for the treatment of hepatitis-C-infected patients under Pegylated-Interferon (PEG-IFN-α 2b ) 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.

Observer‐based controller for treatment of hepatitis C infection using fractional order model

“…In these works, objective functions have been considered to minimize viral load, infected cells, and drug side effects. In other works, [41][42][43] appropriate Lyapunov functions have been utilized to design stable control strategies for the disease to reduce the viral load or infected cells to their desired value. In all of the mentioned works, IO models have been utilized to design the treatment method.…”

“…Due to the dangers of the disease progress towards liver cancer and death, many researches have been carried out to propose effective treatment strategies for HCV infection by using different control strategies. [36][37][38][39][40][41][42][43] In previous works, [36][37][38][39][40] offline optimal control has been utilized to design effective methods for the HCV treatment. In these works, objective functions have been considered to minimize viral load, infected cells, and drug side effects.…”

“…Input saturation is one of the input nonlinearities that occurs in most of the systems, and some methods have been proposed for handling this limitation in the controller design. 41,[47][48][49][50][51][52] Utilizing first order filters in the backstepping method, 47,48 using the mean-value theorem, 49,50 defining the saturated control law in a convex hull, 51 and considering a special form for the state feedback controller gain 41,52 are some methods for handling this type of input nonlinearity in the controller design for IO and FO systems.…”

“…Due to the dangers of the disease progress towards liver cancer and death, many researches have been carried out to propose effective treatment strategies for HCV infection by using different control strategies 36–43 . In previous works, 36–40 offline optimal control has been utilized to design effective methods for the HCV treatment.…”

Design a robust sliding mode controller based on the state and parameter estimation for the nonlinear epidemiological model of Covid-19

“…In the last year, the design of a controller for the nonlinear epidemiological model of Covid-19 turns into a popular topic [35][36][37][38][39]. In [40], the authors proposed an optimal controller based on the Pontryagin principle to mitigate the spread of Covid-19.…”