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 , Ahmad Fakharian ² , Rezvan Abbasi ³

1 - Department of Electrical, Biomedical and Mechatronics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - Department of Electrical Engineering, Qazvin Branch, Islamic Azad University
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.

References:

. Ortega R, et al. Passivity-based Control of Euler-Lagrange Systems. London: Springer-Verlag, 1998.
. Ortega R and Spong M. Adaptive motion control of rigid robots: a tutorial. Automatica 1989; 25: 877-888.
. Gorji S, Fakharian A and Abbasi R. Virtually Euler-Lagrange form for feedback passivation of a wide range of non-Euler-Lagrange systems: Adaptive Passivity-Based Control of Hepatitis B Disease. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2023; 237: 1-18.
. Shim H. A Passivity-based Nonlinear Observer and a Semi-global Separation Principle. PhD Thesis, Seoul National University, 2000.
. Pare TE. Passivity-based analysis and control of nonlinear systems. PhD Thesis, Stanford University, 2000.
. Ali M and Alexander CK. Robust tracking control of a robot manipulator using a passivity-based extended-state observer approach. IET Cyber-syst Robot 2019; 1: 63-71.
. Bouakrif F, Boukhetala D and Boudjema F. Passivity-based controller-observer for robot manipulators. 3rd International Conference on Information and Communication Technologies: From Theory to Applications, Damascus, Syria, 7-11 April. 2008.
. Peiris LDH, Du Bois JL and Plummer AR. Passivity-based adaptive delay compensation for real-time hybrid tests. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2020; 235: 427-432.
. Salim R, et al. Sensorless passivity based control for induction motor via an adaptive Observer. ISA Transactions 2019; 84: 118-127.
. Liu Y, et al. Passivity Control of Induction Motors based on Adaptive Observer Design. 3rd IFAC International Conference on Intelligent Control and Automation Science, Chengdu, China, 2-4 Sep. 2013, pp. 176-181.
. Salamat B and Tonello AM. Energy Based Control of a Swash Mass Helicopter through Decoupling Change of Coordinates. IEEE Access 2020; 8: 77449-77458.
. Salamat B and Tonello AM. A Swash Mass Pendulum with Passivity-Based Control. IEEE Robotics and Automation Letters 2021; 6: 199-206.
. Tiitinen L, Hinkkanen M and Harnefors L. Stable and Passive Observer-Based V/Hz Control for Induction Motors. IEEE Energy Conversion Congress and Exposition, Detroit, MI, USA, 9-13 Oct. 2022, pp. 1-8.
. Brogliato B, Lozano R, et al. Dissipative systems analysis and control. 3rd ed. Switzerland AG: Springer Nature, 2020.
. Salimifard M and Talebi HA. Robust output feedback fault-tolerant control of non-linear multi-agent systems based on wavelet neural networks. IET Control Theory & Applications 2017; 11: 3004-3015.
. Rajamani R and Cho Y. M. Existence and design of observers for nonlinear systems: relation to distance to unobservability. International Journal of Control 1998; 69: 717-731.
. Rajamani R. Observers for Lipschitz Nonlinear Systems. IEEE Transaction on Automatic Control 1998; 43: 397-401.
. Dong Y, Liu W and Liang S. Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties. International Journal of Robust and Nonlinear Control 2017; 27: 1974-1998.
. Raïssi T, Efimov D and Zolghadri A. Interval state estimation for a class of nonlinear systems. IEEE Trans. Automatic Control 2012; 57: 260-265.
. Raïssi T, Videau G and Zolghadri A. Interval observers design for consistency checks of nonlinear continuous-time systems. Automatica 2010; 46: 518-527.
. Efimov D, et al. Interval State Observer for Nonlinear Time Varying Systems. Automatica 2013; 49: 200-205.
. Manzoor S, et al. Hepatitis B virus therapy: What’s the future holding for us?. World J. Gastroenterol 2015; 21: 12558-12575.
. World Health Organization. Online Referencing, http://www.who.int.
. Jang J. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences and Engineering 2018; 15: 667-691.
. Ding Y and Wang WJ. Control strategy design for the anti-HBV mathematical model. IET Syst. Biol. 2019; 13: 186-193.
. Aghajanzadeh O, et al. Robust adaptive Lyapunov-based control of hepatitis B infection. IET Syst. Biol. 2018; 12: 62-67.
. Aghajanzadeh O, et al. Nonlinear Adaptive Control Method for Treatment of Uncertain Hepatitis B Virus Infection. Biomedical Signal Processing and Control 2017; 38: 174-181.
. Aghajanzadeh O, Sharifi M and Falsafi A. Robust control strategy for HBV treatment: Considering parametric and nonparametric uncertainties. Control Applications for Biomedical Engineering Systems 2020; 5: 127-147.
. Slotin JJE and Li W. Applied nonlinear control. Englewood Cliffs, NJ: Prentice Hall, 1991.
. Sheikhan M and Ghoreishi SA. Antiviral therapy using a fuzzy controller optimized by modified evolutionary algorithms: a comparative study. Neural Computing and Applications 2013; 23: 1801-1813.
. Nowak MA, et al. Viral dynamics in hepatitis B virus infection. Proceedings of the National Academy of Sciences 1996; 93: 4398-4402.