Dynamical analysis and anti-oscillation-based adaptive control of the FO arch MEMS with optimality

This paper mainly investigates dynamical analysis and anti-oscillation-based adaptive control issues of the fractional-order (FO) arch microelectromechanical system (MEMS) with optimality. With the aid of phase diagram and Lyapunov exponent, the dynamical analysis reveals that chaotic oscillation originated in non-equilibrium interaction of potential energy can deteriorate the performance of the FO arch MEMS under different FOs and excitation amplitudes. During the design process, a recurrent non-singleton type-2 fuzzy neural network with a transformation is employed to approximate uncertain function and the Nussbaum function is used to tackle the problem of unknown control direction from actuation characteristic in the field of Caputo fractional derivative. Meanwhile, a tracking differentiator based on the hyperbolic sine function is designed to solve the repeated differentiation of virtual control because of complicated FO calculation. Then, an anti-oscillation-based adaptive control scheme fused with the Nussbaum function, neural network, tracking differentiator and optimal control is developed in the framework of backstepping by means of continuous frequency distributed model. The asymptotic stability of the proposed solution is proved based on the Lyapunov stability criterion. Finally, simulation results validate the feasibility of the presented scheme under multi-step methods of numerical solution.