Dynamical analysis and event-triggered adaptive finite-time prescribed performance control of the FO coupled MEMS resonators

This paper explores the dynamic behaviors and control method of weakly coupled micro-electro-mechanical system (MEMS) resonators with fractional-order (FO) dynamics. In the dynamics analysis session, Lyapunov exponents, bifurcation theory, and phase diagrams are used to analyze the effects of system parameters, coupling stiffness, and FO on the complex dynamical behaviors such as periodicity, pseudo-periodicity, and chaos oscillations. To suppress chaotic oscillations, a dynamic event-triggered finite-time prescribed performance controller is proposed. The unknown nonlinear functions are approximated through the interval type-3 fuzzy system (IT3FS) with an adaptive law. A novel finite-time prescribed performance function (finite-time PPF) is constructed to establish constrained boundaries for tracking errors. Compared with the existing PPFs, the proposed approach allows for more flexible setting of the convergence boundary before reaching steady-state. Subsequently, the constrained tracking errors are mapped to an unconstrained form using a nonlinear transformation function, whether the error constraint is symmetric or asymmetric. To circumvent the "explosion of complexity" arising from backstepping design process, a tracking differentiator (TD) is utilized. Additionally, to alleviate strain on communication resources, an event-triggered mechanism is devised to update control signals. The trigger threshold of the control signals can be adaptively adjusted based on the values of the Lyapunov function and the dynamic auxiliary variables. This control method guarantees finite-time convergence for all signals of the system. Finally, extensive simulations are performed to verify the effectiveness of the proposed algorithm.