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Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. (English) Zbl 1219.93023
Summary: The problem of finite-time chaos synchronization between two different chaotic systems with fully unknown parameters is investigated. First, a new nonsingular terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is proved. Then, appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Afterwards, based on the adaptive laws and finite-time control idea, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, some numerical simulations are presented to demonstrate the applicability and effectiveness of the proposed technique.

MSC:
93B12 Variable structure systems
34H10 Chaos control for problems involving ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93D15 Stabilization of systems by feedback
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