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Robust adaptive multi-switching synchronization of multiple different orders unknown chaotic systems. (English) Zbl 1455.93144

Summary: Multi-switching synchronization (MSS) of multiple different orders unknown chaotic (UC) systems confines hacking in the digital transmission process. Similarly, the suppression of undesirable chattering increases synchronization performance. This paper proposes a new robust synchronization control (RASC) technique and discusses the MSS of multiple different orders UC systems. This controller accomplishes (i) quick convergence, (ii) reduces the transient oscillations, and (iii) the rate of convergence decreases in the vicinity of the origin that causes the suppression of chattering. Analysis based on the Lyapunov direct method assures this convergence behavior with any positive values of the feedback gains. This work also provides parameters updated law that estimates the true values of unknown parameters. Numerical examples of five UC systems different orders are simulated. The computer based graphical results validate the efficiency and performance of the proposed RASC technique and the synchronization strategy when compare to peer works. In the simulation, the proposed synchronization strategy successfully recovers an encrypted received image on a communication channel. The article suggests some future research problems to extend the use of the proposed work.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C40 Adaptive control/observation systems
93B35 Sensitivity (robustness)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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