Dynamical analysis and predefined finite-time backstepping control for a small network consisting four coupled MEMS resonators

This paper investigates dynamical analysis and predefined finite-time backstepping control for a small network consisting four coupled MEMS resonators. Firstly, a novel small network structure of coupled MEMS resonators is proposed to enhance sensitivity and bandwidth, and its corresponding mathematical model is established. Secondly, a detailed dynamic analysis is conducted to examine the influence of system parameters, including the applied alternating voltage, on the system's behavior. The results reveal that chaotic oscillations become more severe as the applied alternating voltage increases a little or exceeds a critical coupling threshold. Thirdly, to suppress these detrimental chaotic oscillations and simultaneously achieve high-performance control, a predefined finite-time backstepping control strategy is developed. The approach incorporates a predefined performance function to transform the state-constraint problem into a boundedness problem involving newly defined variables. A type-2 sequential fuzzy neural network (T2SFNN) is used to approximate unknown nonlinear functions, and an improved accelerated exponential integral tracking differentiator (AEITD) is employed to resolve the differential explosion issue in the backstepping design. Rigorous stability analysis confirms that all closed-loop signals remain bounded and the tracking errors stay within a prescribed range. Finally, extensive simulation results demonstrate the feasibility, robustness and superiority of the proposed approach.