Chaos Analysis-Based Adaptive Backstepping Control of the Microelectromechanical Resonators with Constrained Output and Uncertain Time Delay

This paper focuses on chaos analysis-based adaptive backstepping control of the microelectromechanical resonators. To better understand the deep-rooted operational mechanism, the bifurcation diagram, phase diagrams, and corresponding time histories are presented to analyze the nonlinear dynamics and chaotic behavior of the microelectromechanical resonators. Based on the potential function, it can be shown that the microelectromechanical resonators undergo homoclinic and heteroclinic orbits which relate closely to the appearance of chaos in the resonator response. To suppress chaos and vibration, an adaptive neural network-based backstepping scheme is developed to tune the random motion into regular motion without the need for more precise information of system model. The tangent barrier Lyapunov function is used to develop a control scheme for the microelectromechanical resonators capable of preventing output constraint violation. By using tracking differentiator in controller design, the 'explosion of complexity' of backstepping and poor precision of the first-order filters is prevented. Meanwhile, to increase the robustness and adaptivity, an adaptive neural network is employed to approximate uncertain nonlinear item in the framework of backstepping. Finally, numerical simulations are conducted to validate the effectiveness and robustness of the proposed approach.