Fractional High-Order Differential Estimator and Feedback Controller Design for a Single-Input-Single-Output Affine Chaotic System

Şahin E., Ayas M. Ş.

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, vol.15, no.1, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1115/1.4045404
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, Metadex, Civil Engineering Abstracts
  • Karadeniz Technical University Affiliated: Yes


Control of chaos generally refers to realize a desired behavior of chaotic system output and its states. In this manner, we design a fractional high-order differential feedback controller (FHODFC) to increase tracking performance of a nonlinear system output and its differentials for a desired trajectory signal. The proposed controller is based on fractional calculus and high-order extracted differentials of error signal. The suggested fractional approach is applied to a single-input-single-output affine Duffing-Holmes dynamical system in matlab/simulink environment. Duffing-Holmes system is analyzed for two different problems: estimation and control problems. The simulation results clearly demonstrate superior dynamic behavior of the FHODFC compared to the classical high-order differential feedback controller (HODFC) version for both estimation and control problems.