Passivity-based design of controller and observer for a class of nonlinear systems with application to Hepatitis B Disease

Subject Areas : Electrical Engineering

shaghayegh gorji ¹ (Department of Electrical, Biomedical and Mechatronics, Qazvin Branch, Islamic Azad University, Qazvin, Iran)
Ahmad Fakharian ² (Department of Electrical Engineering, Qazvin Branch, Islamic Azad University)
Rezvan Abbasi ³ (Department of Electrical Engineering, Qazvin Branch, Islamic Azad University)

Received: 2024-03-24 Accepted : 2024-04-17 Published : 2024-04-24

Keywords: passivity-based design, state-observer, adaptive control, Lipschitz nonlinear systems, virtually Euler-Lagrange, hepatitis B virus,

Abstract :

In this paper, a strictly passive formulation has been developed to design a passive state-observer for both time-invariant and time-varying Lipschitz nonlinear systems. During this formulation, a convergence and strictly passive state-observer is provided to have passive closed-loop system. Some definitions and charts are defined here for time-invariant and time-varying systems in different scenarios. A new interconnection between passivity of subsystems and passivity/stability of the closed-loop system has been introduced from a different point of view. All definitions are organized based on the systematic method called “virtually Euler-Lagrange” form of passivation. Utilizing this form and theses definitions, make the design process simpler and straightforward, while, some conditions of design will be released due to using these definitions. The designed controller/observer has been applied to control the hepatitis B virus infection disease. The reliability of the proposed definitions are examined by using MATLAB/SIMULINK, while, the results demonstrate the ability and power of this novel approach.

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