Abstract
We propose novel controllers for stabilization and tracking of chaotic and hyperchaotic Lorenz systems using extended backstepping techniques. Based on the proposed approach, generalized weighted controllers were designed to control chaotic behaviour as well as to achieve synchronization in chaotic and hyperchaotic Lorenz systems. The effectiveness and feasibility of the proposed weighted controllers were verified numerically and showed their robustness against noise.
Highlights
Chaos theory has found application in many areas of studies; these include mathematics, physics, biology, engineering, economics, and politics [1,2,3]
In order to reduce the complexity in controllers and energy consumption, the present work is focused on the design of generalized weighted controllers for stabilization and tracking of chaotic and hyperchaotic systems using extended backstepping method
The proposed extended backstepping controllers can produce economic controllers with low energy consumption which may be suitable for practical implementation
Summary
Chaos theory has found application in many areas of studies; these include mathematics, physics, biology, engineering, economics, and politics [1,2,3]. A wide variety of approaches have been proposed to achieve chaos synchronization in the coupled/forced chaotic systems such as linear state error feedback method [11], time-delay feedback method [12], active control approach [13, 14], impulsive method [15], adaptive control [16, 17], and backstepping approach [18]. In order to reduce the complexity in controllers and energy consumption, the present work is focused on the design of generalized weighted controllers for stabilization and tracking of chaotic and hyperchaotic systems using extended backstepping method. Based on this approach, controller complexity is minimized and controller is singularity free from nonlinear quadratic terms [7, 11]. The approach may be suitable for practical implementation in some real systems
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
