Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances

Alain Soup Tewa KAMMOGNE; Michaux Noubé KOUNTCHOU; Romanic KENGNE; Ahmad Taher AZAR; Hilaire Bertrand FOTSIN; Soup Teoua Michael OUAGNI

doi:10.1631/FITEE.1900430

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Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances

Regular Papers | Updated：2022-05-19

- Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances
- 基于多项式鲁棒观测器实现结构扰动下非线性分数阶系统被动式同步
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 9, Pages: 1369-1386(2020)
- Affiliations：
  
  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
  Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 11586, Saudi Arabia
  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
- Author bio：
  
  Alain Soup Tewa KAMMOGNE, E-mail: kouaneteoua@yahoo.fr
  [ "Ahmad Taher AZAR, E-mail: aazar@psu.edu.sa; ahmad.azar@fci.bu.edu.eg" ]
- Funds：
- DOI：10.1631/FITEE.1900430
  CLC： TP273;O415
- Received：24 August 2019，
  
  Revised：2020-;8-;5，
  
  Published：2020-09
- Accepted：
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Alain Soup Tewa KAMMOGNE, Michaux Noubé KOUNTCHOU, Romanic KENGNE, et al. Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1369-1386.
DOI：

Alain Soup Tewa KAMMOGNE, Michaux Noubé KOUNTCHOU, Romanic KENGNE, et al. Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1369-1386. DOI： 10.1631/FITEE.1900430.

摘要

基于对一类具有不匹配的不确定性和扰动的分数阶Colpitts（fractional-order Colpitts，FOC）系统的无源同步，设计一种鲁棒的多项式观测器，以最小化未知的有界干扰对误差估计的影响。利用自适应多项式状态观测器，提出一种更实用的输出反馈无源控制器，采用FOC连续频率分布式方法分析观测器的稳定性。基于分数阶Lyapunov稳定性理论，结合Finsler引理，构造鲁棒无源同步的严格条件。所提方法保证了控制器的渐近稳定性，且所导出的自适应律能够消除非线性对象动力学的不确定性。使用PSpice对整个系统作仿真，以证实所提控制方案的可行性。对分数阶混沌Colpitts系统中控制问题的仿真分析表明，该方法为一大类非线性分数阶导数系统构建了高效且系统的控制过程。

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.

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