Adaptive Synchronization of the Fractional-Order Chaotic Arch Micro-Electro-Mechanical System via Chebyshev Neural Network

Aimed at the synchronization issue between the drive system and response system of the fractional-order chaotic arch micro-electro-mechanical system under distributed electrostatic actuation, we propose an adaptive synchronization scheme which combines the best of the Chebyshev neural network, extended state tracking differentiator and adaptive backstepping. To compensate uncertainties and time delay existing in the control system, a Chebyshev neural network with a weight is applied to approximate uncertain item in the synchronization error vector while its weight is tuned by a fractional-order adaptive law online. Introducing an extended state tracking differentiator avoids repeated derivative of the virtual control. Based on the fractional-order Lyapunov stability criterion, the stability of the closed fractional-order arch micro-electromechanical system is guaranteed. Finally, the effectiveness of the proposed adaptive synchronization scheme for the fractional-order chaotic arch micro-electro-mechanical system is demonstrated through simulation results.