TY - JOUR
T1 - Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders
AU - Ahmad, Israr
AU - Shafiq, Muhammad
N1 - Publisher Copyright:
© 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2020/7/2
Y1 - 2020/7/2
N2 - The precise anti-synchronization control of uncertain chaotic systems has always remained an interesting problem. The anti-synchronization control of multiple different orders uncertain chaotic systems increases the complexity and enhances the security of the information signal in secure communications. Hence, it confines the hacking in digital communication systems. This paper proposes a novel adaptive control technique and studies the double combination anti-synchronization of multiple different orders uncertain chaotic systems. The proposed adaptive feedback control technique consists of three fundamental nonlinear components. Each component accomplishes a different objective; (i) stability of the closed-loop, (ii) smooth and fast convergence behaviour of the anti-synchronization error, and (iii) disturbance rejection. The theoretical analysis in (i) to (iii) uses the Lyapunov stability theory. This paper also provides parameters adaptation laws that stabilize the uncertain parameters to some constants. The paper discusses the simulation results of two representative examples of four different orders uncertain chaotic systems. These examples demonstrate anti-synchronization among hyperchaotic Lü, uncertain chaotic Shimizu Morioka, uncertain second-order nonlinear duffing, and uncertain parametrically excited second-order nonlinear pendulum systems. The computer-based simulation results certify the efficiency and performance of the proposed anti-synchronization control approach and compare them with peer works.
AB - The precise anti-synchronization control of uncertain chaotic systems has always remained an interesting problem. The anti-synchronization control of multiple different orders uncertain chaotic systems increases the complexity and enhances the security of the information signal in secure communications. Hence, it confines the hacking in digital communication systems. This paper proposes a novel adaptive control technique and studies the double combination anti-synchronization of multiple different orders uncertain chaotic systems. The proposed adaptive feedback control technique consists of three fundamental nonlinear components. Each component accomplishes a different objective; (i) stability of the closed-loop, (ii) smooth and fast convergence behaviour of the anti-synchronization error, and (iii) disturbance rejection. The theoretical analysis in (i) to (iii) uses the Lyapunov stability theory. This paper also provides parameters adaptation laws that stabilize the uncertain parameters to some constants. The paper discusses the simulation results of two representative examples of four different orders uncertain chaotic systems. These examples demonstrate anti-synchronization among hyperchaotic Lü, uncertain chaotic Shimizu Morioka, uncertain second-order nonlinear duffing, and uncertain parametrically excited second-order nonlinear pendulum systems. The computer-based simulation results certify the efficiency and performance of the proposed anti-synchronization control approach and compare them with peer works.
KW - Lyapunov function
KW - Robust adaptive control
KW - anti-synchronization
KW - chaotic systems
UR - http://www.scopus.com/inward/record.url?scp=85085559230&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85085559230&partnerID=8YFLogxK
U2 - 10.1080/00051144.2020.1765115
DO - 10.1080/00051144.2020.1765115
M3 - Article
AN - SCOPUS:85085559230
SN - 0005-1144
VL - 61
SP - 396
EP - 414
JO - Automatika
JF - Automatika
IS - 3
ER -