This paper analyzes the integration of linear systems and neural networks for the identification and optimal control of weakly nonlinear systems. Considering previous knowledge about the system given by approximated linear state-space equation models and linear controllers, training algorithms for identification and control were derived considering the dynamics of the nonlinear system. It was found that the integrated linear-neuro model can identify the dynamics of the system much more accurately than a purely linear model or a purely neuro model. It was also found that the vibration isolation performance of the system with integrated linear-neuro control is much better than the system with linear control or neuro-control.