Stability Assessment of Direct Neural Control Scheme with Reference Model using Online and Offline Training

A scheme of direct neural network based control with a reference model is considered. The analysis of the neural controller sustainability is made with the help of the Lyapunov second method theorems in case of its offline and online training using the backpropagation method. For offline training, it is shown that such process is stable. But the occurrence of situations, which are not included in the training set, leads to the deterioration of the control quality. This problem can be solved using online training. However, for such a case, it is proved that the boundedness of all neural controller signals and, consequently, the closed loop neuro-control system (i.e. stability) is not guaranteed. The absolute values of the weights and biases of the neural network (controller) can become infinite. The dead zones and various modifications of training equations, e.g. the regularization, can be applied to overcome this problem. But a more correct approach is the derivation of formulas of the neural network online training, which would initially guarantee the stability of the closed control loop. This is the aim of further research.