Abstract
This paper introduces the projective synchronization of different fractional-order multiple chaotic systems with uncertainties, disturbances, unknown parameters, and input nonlinearities. A fractional adaptive sliding surface is suggested to guarantee that more slave systems synchronize with one master system. First, an adaptive sliding mode controller is proposed for the synchronization of fractional-order multiple chaotic systems with unknown parameters and disturbances. Then, the synchronization of fractional-order multiple chaotic systems in the presence of uncertainties and input nonlinearity is obtained. The developed method can be used for many of fractional-order multiple chaotic systems. The bounds of the uncertainties and disturbances are unknown. Suitable adaptive rules are established to overcome the unknown parameters. Based on the fractional Lyapunov theorem, the stability of the suggested technique is proved. Finally, the simulation results demonstrate the feasibility and robustness of our suggested scheme.
Highlights
In the last few years, chaos synchronization of multiple chaotic systems has received considerable attention among scholars in various fields of research
6 Conclusion This work attempts to study the issue of projective synchronization of different fractionalorder multiple chaotic systems with fully uncertain parameters, uncertainties, disturbances, and nonlinear input
In the initial part of the discussion, an adaptive sliding mode controller is suggested for projective synchronization in the presence of uncertain parameters and disturbances
Summary
In the last few years, chaos synchronization of multiple chaotic systems has received considerable attention among scholars in various fields of research. Qin et al in [35] reported a procedure to synchronize unknown fractional-order time-delayed chaotic systems based on adaptive fuzzy control. In [39], the finite-time robust control of uncertain nonlinear fractional-order Hopfield neural networks was studied via adaptive sliding mode control All of these works only examined the synchronization of two chaotic systems. The projective synchronization of fractional-order multiple chaotic systems with unknown parameters and disturbances, where more slave systems synchronize with one master system, is studied. Using the proposed controller, the projective synchronization of fractional-order multiple chaotic systems in the presence of uncertainties, disturbances, and nonlinear input is investigated. 3.1 Problem statement we utilize the adaptive sliding mode control technique to obtain projective synchronization of fractional-order multiple chaotic systems in the presence of uncertain parameters and disturbances. Assumption 2 The constants σ1i, θji, and ρi are unknown positive
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