A novel neural network architecture, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable structure neural network, the number of basis functions can be either increased or decreased with time according to specified design strategies so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive state feedback controller is presented. The location of the centers of the GRBFs is analyzed using a new method inspired from evolutionary artificial potential fields method combined with a pruning algorithm. Using this method we can guarantee a minimal number of neuron. It is in noted, that both the recruitment and the pruning is made by a single neuron. Consequently, the recruitment phase does not perturb the network and the pruning does not provoke an oscillation of the output response. The weights of neural network are adapted using a Lyapunov approach. Moreover, the stability of the system can be analyzed and guaranteed by introducing the supervisory controller and modified adaptation law with projection.