Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with struc
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Frontiers of Information Technology & Electronic Engineering www.jzus.zju.edu.cn; engineering.cae.cn; www.springerlink.com ISSN 2095-9184 (print); ISSN 2095-9230 (online) E-mail: [email protected]
Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances Alain Soup Tewa KAMMOGNE†‡1, Michaux Noubé KOUNTCHOU2, Romanic KENGNE1, Ahmad Taher AZAR†3,4, Hilaire Bertrand FOTSIN1, Soup Teoua Michael OUAGNI5 1 2
LAMACETS, Faculty of Sciences, University of Dschang, P.O. Box 96, Cameroon
Nuclear Technology Section, Institute of Geological and Mining Research, P.O. Box 4110, Yaoundé, Cameroon 3
Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 11586, Saudi Arabia 4 5
Faculty of Computers and Artificial Intelligence, Benha University, Benha 13511, Egypt
Laboratoire de Mécanique et de Modélisation des Systèmes Physique, Faculty of Sciences, University of Dschang, P.O. Box 96, Cameroon †
E-mail: [email protected]; [email protected]; [email protected]
Received Aug. 24, 2019; Revision accepted May 17, 2020; Crosschecked Aug. 5, 2020
Abstract: A robust polynomial observer is designed based on passive synchronization of a given class of fractional-order Colpitts (FOC) systems with mismatched uncertainties and disturbances. The primary objective of the proposed observer is to minimize the effects of unknown bounded disturbances on the estimation of errors. A more practicable output-feedback passive controller is proposed using an adaptive polynomial state observer. The distributed approach of a continuous frequency of the FOC is considered to analyze the stability of the observer. Then we derive some stringent conditions for the robust passive synchronization using Finsler’s lemma based on the fractional Lyapunov stability theory. It is shown that the proposed method not only guarantees the asymptotic stability of the controller but also allows the derived adaptation law to remove the uncertainties within the nonlinear plant’s dynamics. The entire system using passivity is implemented with details in PSpice to demonstrate the feasibility of the proposed control scheme. The results of this research are illustrated using computer simulations for the control problem of the fractional-order chaotic Colpitts system. The proposed approach depicts an efficient and systematic control procedure for a large class of nonlinear systems with the fractional derivative. Key words: Robust passive observer; Adaptive synchronization; Lyapunov theory; Fractional-order; Polynomial observer; Uncertain parameters; H∞-performance https://doi.org/10.1631/FITEE.1900430 CLC number: TP273; O415
1 Introduction In many engineering problems, different approaches used in controlling nonlinear systems can be more easily understood using fractional-order deriv‡
Corresponding author ORCID: Alain Soup Tewa KAMMOGNE, https://orcid.org/00000003-0234-8652; Ahmad Taher AZAR, https://orcid.org/0000-00027869-6373 © Zhejiang University and Sprin
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