In the optimization of the trajectory or of the guidance of mobile robots one of the more important things is to assure one small difference between the output data of the system and the target. This paper show how on-line will be possible to establish one convergence way to the target without any influences of the input data or initial conditions of the weights or biases. The paper show the general components and the mathematical model of some more important neurons and one numerical simulation of the linear neural network. In the paper was used the least mean square (LMS) error algorithm for adjusting the weights and biases and incremental training by different training rate, finally to obtain one minimum error to the target.