Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders

Israr Ahmad*, Muhammad Shafiq

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)396-414
Number of pages19
Issue number3
Publication statusPublished - Jul 2 2020


  • Lyapunov function
  • Robust adaptive control
  • anti-synchronization
  • chaotic systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science


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