The invention discloses an adaptive neural network control method for an arc micro-electromechanical system, which comprises the steps of a, building a system model of the arc micro-electromechanicalsystem based on the Bernoulli beam; b, constructing an adaptive neural network controller used for suppressing chaotic oscillation of the arc micro-electromechanical system and guaranteeing state constraints of the system, wherein when the adaptive neural network controller is constructed, output constraints of the arc micro-electromechanical system are ensured not to be violated by using a symmetrical obstacle Lyapunov function, an unknown non-linear function is estimated with an arbitrary small error by adopting an RBF neural network with an adaptive law, an extension state tracking differentiator is introduced to process a problem that virtual control items in backstepping control need to be derived repeatedly, a state observer is designed to obtain unmeasured state information, the extension state tracking differentiator and the state observer are integrated in the backstepping framework. The adaptive neural network control method has the characteristics of convenient stability analysis and proving, low requirement for the modeling precision, low computation complexity, high operation speed, good operation stability of the system and high motion accuracy.