A microgrid consists of a variety of inverter-interfaced distributed energy resources (DERs). A key issue is how to control DERs within the microgrid and how to connect them to or disconnect them from the microgrid quickly. This paper presents a strategy for controlling inverter-interfaced DERs within a microgrid using an artificial neural network, which implements a dynamic programming algorithm and is trained with a new Levenberg-Marquardt backpropagation algorithm. Compared to conventional control methods, our neural network controller exhibits fast response time, low overshoot, and, in general, the best performance. In particular, the neural network controller can quickly connect or disconnect inverter-interfaced DERs without the need for a synchronization controller, efficiently track fast-changing reference commands, tolerate system disturbances, and satisfy control requirements at grid-connected mode, islanding mode, and their transition.