The application of adaptive control algorithms for vibration suppression of smart structures is investigated in this paper. An accurate mathematical representation is not required in this approach. The controller adapts to the parameter variations of the structural system by updating the controller gains. When the desired performance of an unknown plant with respect to an input signal can be specified in the form of a linear or a non-linear differential equation, stable control can be achieved using model-reference adaptive control (MRAC) techniques. The conventional MRAC techniques have been successfully implemented on a smart-structure test article resulting in perfect model following. We have also investigated the design of neural-network-based adaptive control system for smart structures. Two neural networks, one for system identification and another for control purposes, are needed for the implementation of adaptive controllers, In this paper, a direct variable model identification technique using neural networks has been developed. An iterative inversion of a neural model of the forward dynamics of the plant has been utilized for the implementation of a neural controller. This algorithm generates a smooth control. We have also developed an adaptive neuron activation function for reducing the learning time of neural networks. The performance of the neural-network-based adaptive controllers has been verified using simulation studies.