Artificial Neural Networks have gained increasing applications in the area of control in recent years. This article outlines a neural network based identification and optimal control approach for a specific nonlinear system that consists of a cantilever plate. The neural networks employed are multi-layer perceptrons with backpropagation learning method. The identifier is implemented in time domain to represent system nonlinearities. Backpropagation method is chosen so that the Jacobian of the system dynamics can be acquired directly and utilized later in obtaining the optimal control. The controller is designed to minimize a finite horizon quadratic cost function by solving the Hamiltonian equations. In order to compensate for the error accumulation between the model and the real system, the receding horizon control method is implemented.