Stable weights dynamics for a class of differential neural network observer

The most important aspect of differential neural networks dynamics is related to their weights properties. This is a consequence of the complex non-linear structure describing the learning matrix differential equations, which are associated with adaptive capability of this kind of neural network. So far, there is no analytical demonstration about the weights stability. In fact, this is the main inconvenience in designing real applications for differential neural network observers. This study deals with the stability proof for the weights dynamics using an adaptive procedure to adjust the weights ordinary differential equations. Three different examples (two of them were realised by numerical simulations and the last one was carried out using real biofiltering process data) demonstrated the good performance of the suggested approach.