Chaos synchronization of an electrostatic MEMS resonator in the presence of parametric uncertainties

This paper addresses the synchronization control problem of a class of chaotic systems. The synchronization is obtained by using an adaptive control law, which guaranties a global asymptotical convergence of the error between the outputs of driving and response systems in the presence of parametric uncertainties in both systems. The method of synchronization can be applied to a wide class of systems though the present work focuses only on a particular case, mainly, Micro Electro Mechanical Systems (MEMS). As an example of application, an electrostatic MEMS resonator with unknown damping and stiffness actions is synchronized with a Duffing chaotic oscillator and a MEMS chaotic oscillator. This component can be used in such applications as secure communication. Numerical simulations are carried out to confirm the validity of the developed control schemes.