This paper proposes an adaptive observer-based scheme to control fractional-order chaotic micro-electro-mechanical-systems (MEMS). The fractional-order model of a system exhibits the dynamic behaviour of a physical system more accurately than a similar integer-order one. An observer-based control considering the unknown parameters is presented for a fractional-order chaotic micro-electro-mechanical-system. To handle the existence of the unknown parameters, the control law consists of both estimated parameters and also estimated states that have been designed. First, a fractional-order observer is designed to estimate the state variables. The asymptotic convergence to zero of the estimation state error is proved using the Lyapunov scheme. After that, with the designed observer as a foundation, adaptive control is expanded for the closed-loop system to ensure its asymptotic stability. An evaluation of the proposed method shows its efficacy via simulations for two case studies.
