Page 589 - Mathematical Techniques of Fractional Order Systems

Chapter 19

Control and Synchronization of

a Fractional Order Hyperchaotic
System via Backstepping and

Active Backstepping Approach

1
1,2
Manoj K. Shukla , Bharat B. Sharma and Ahmad Taher Azar 3,4
1 2
National Institute of Technology, Hamirpur, Himachal Pradesh, India, Lovely Professional
3
University, Punjab, India, Faculty of Computers and Information, Benha University, Benha,
4
Egypt, School of Engineering and Applied Sciences, Nile University, Giza, Egypt
19.1 INTRODUCTION
Many physical phenomena have an intrinsic fractional order description and so
fractional order calculus is necessary to replicate their input output character-
istics. Fractional calculus finds wide application in different unrelated topics
such as: transmission line theory, chemical analysis of aqueous solutions, vis-
coelasticity, electromagnetic wave, quantum mechanical calculations, signal
processing, robotics, bioengineering, control systems, etc. The incorporation of
two degrees of freedom from the use of a fractional order integrator and differ-
entiator provides a greater degree of flexibility and hence makes it possible to
further improve the performance of traditional PID controllers. Fractional order
calculus allows us to describe and model a real system, more accurately than
the classical integer methods, which further enables us to analyze them in a
better way and design better controllers. Fractional order chaotic system can be
helpful in random number generation and more secure communication.
The additional parameters of differintegral orders give more flexibility to the
designer. Fractional derivatives provide an excellent instrument for the descrip-
tion of memory and hereditary properties of various materials and processes.

19.1.1 Introduction to Chaotic Systems

Nonlinear systems are very interesting to engineers, physicists, and mathe-
maticians because most real physical systems are inherently nonlinear in

Mathematical Techniques of Fractional Order Systems. DOI: https://doi.org/10.1016/B978-0-12-813592-1.00019-2
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