AUTHOR=Chen Youjun , Wang Feng 

TITLE=Disturbance observer based adaptive fuzzy synchronization controller design for uncertain fractional-order chaotic systems

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 8 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.1019047

DOI=10.3389/fams.2022.1019047

ISSN=2297-4687

ABSTRACT=To control uncertain strict-feedback  chaotic systems, the adaptive  backstepping technique is a popular method, yet this method requires repeatedly differentiating virtual control inputs, which will result in the ``explosion of complexity''  problem. In this paper, an alternative control method for uncertain strict-feedback   chaotic systems without using backstepping technique is presented.  We first translate the uncertain strict-feedback   chaotic system into a new straightforward normative system whose states are unmeasurable, and then, an observer is designed to estimate the unknown states of the transformed system. A new recurrent neural network, namely fuzzy echo state network (FESN), is constructed to approximate the lumped uncertainty of the normative system.  The semi-globally stability of the closed-loop system can be guaranteed by the FESN sliding mode controller that only uses one FESN and one adaptation law. Comparative simulations are put forward to verify the  derived theoretical results.