Dynamics and Improved Robust Adaptive Control Strategy for the Finite Time Synchronization of Uncertain Nonlinear Systems

This letter addresses a robust adaptive control for the synchronization method based on a modified polynomial observer (slave system) which tends to follow exponentially the chaotic Colpitts circuits brought back to a topology of the Chua oscillator (master system) with perturbations. The authors derive some less stringent conditions for the exponential and asymptotic stability of adaptive robust control systems at finite time. They provide a proof of stability and convergence (hence, that synchronization takes place) via Lyapunov stability method. That is, the observer (slave system) must synchronize albeit noisy measurements and reject the effect of perturbations on the system dynamics. To highlight their contribution, the authors also present some simulation results with the purpose to compare the proposed method to the classical polynomial observer. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.