A nonlinear control strategy involving a geometric feedback controller utilizing linearized models and neural networks, approximating the higher order terms, is presented. Online adaptation of the network is performed using steepest descent with a dead zone function. Closed-loop Lyapunov stability analysis for this system has been proven, where it was shown that the output tracking error was confined to a region of a ball, the size of which depends on the accuracy of the neural network models. The proposed strategy is applied to two case studies for set-point tracking and disturbance rejection. The results show good tracking comparable to that when the actual model of the plant is utilized and better than that obtained when the linearized models or neural networks are used alone. A comparison was also made with the conventional proportional-integral-derivative approach.