This paper presents an observer backstepping control strategy to achieve finite-time Chaos Synchronization for uncertain Lorenz system. To compensate for unknown behavior dynamics, radial basis function neural networks (RBFNN) is employed to approximate the uncertain terms system depending on the slave behavior of the system independent of the master system and adaptive laws are derived to update the network weight online within the Lyapunov framework. The authors use Lyapunov stability theory analysis to design an observer controller that ensures the synchronization error converges to zero in a finite-time even with unknown system parameters constants and external disturbances. The effectiveness of the proposed method is demonstrated through numerical simulations.
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