The topic of nonlinear control design has attracted particular attention to satisfy the demanding requirements of recent real-world applications. In this article, a neural network based controller which optimizes a finite horizon quadratic cost function is developed for a class of nonlinear systems with unknown dynamics. Two new types of controllers with different iterative schemes are introduced to converge to the optimal trajectories. To apply such controllers, the system is first modeled using neural networks with back-propogation learning mentod. Both the controllers require the Jacobian matrices of the system state-equations which are obtained directly from the neural network learning process. To test the two control methods, a nonlinear sample system and a physical nonlinear system, a vibrating plate, are used.