Page 626 - Mathematical Techniques of Fractional Order Systems

Chapter 20

Enhanced Fractional Order

Indirect Fuzzy Adaptive
Synchronization of Uncertain

Fractional Chaotic Systems
Based on the Variable Structure

Control: Robust H N Design
Approach

1
2
Khatir Khettab , Yassine Bensafia , Bachir Bourouba 3
and Ahmad Taher Azar 4,5
1 2
Mohamed Boudiaf University of M’sila, M’sila 28000, Algeria, Mohand Oulhadj University of
4
3
Bouira, Bouira 10000, Algeria, University of Se ´tif, Se ´tif 19000, Algeria, Faculty of Computers
5
and Information, Benha University, Benha, Egypt, School of Engineering and Applied Sciences,
Nile University, Giza, Egypt
20.1 INTRODUCTION
Recently, there are many important developments related to the design of non-
linear systems for many practical applications. Several approaches have been
developed such as optimal control, nonlinear feedback control, adaptive con-
trol, sliding mode control, nonlinear dynamics, chaos control, chaos synchroni-
zation control, fuzzy logic control, fuzzy adaptive control, fractional order
control, and robust control and their integrations (Azar & Vaidyanathan,
2015a,b,c, 2016; Azar & Zhu, 2015; Boulkroune et al, 2016a,b; Azar &
Serrano, 2015a,b,c,d, 2016a,b, 2017; Azar et al., 2017a,b,c,d; Azar 2010a,b,
2012; Mekki et al., 2015; Vaidyanathan & Azar, 2015a,b,c,d, 2016a,b,c,d,e,f,
g; Vaidyanathan et al., 2017a,b,c; Zhu & Azar, 2015; Grassi et al., 2017;
Ouannas et al., 2016a, 2017f,g,h,j; Singh et al., 2017; Vaidyanathan et al,
2015a,b,c; Wang et al., 2017).
In recent years, fractional calculus has been applied in the modeling and
control of various kinds of physical systems, as is well known and

Mathematical Techniques of Fractional Order Systems. DOI: https://doi.org/10.1016/B978-0-12-813592-1.00020-9
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