Differential Neural Networks for Identification and Filtering in Nonlinear Dynamic Games

This paper deals with the problem of identifying and filtering a class of continuous-time nonlinear dynamic games (nonlinear differential games) subject to additive and undesired deterministic perturbations. Moreover, the mathematical model of this class is completely unknown with the exception of the control actions of each player, and even though the deterministic noises are known, their power (or their effect) is not. Therefore, two differential neural networks are designed in order to obtain a feedback (perfect state) information pattern for the mentioned class of games. In this way, the stability conditions for two state identification errors and for a filtering error are established, the upper bounds of these errors are obtained, and two new learning laws for each neural network are suggested. Finally, an illustrating example shows the applicability of this approach.