Differential neural network identifier with composite learning laws for uncertain nonlinear systems

This manuscript describes the design and numerical implementation of a novel composite differential neural network aimed to estimate nonlinear uncertain systems. A differential neural network (DNN) with a composite feedback matrix approximates the structure of non-linear uncertain systems. The feedback matrix is assumed to belong to a convex set as well as the free parameters of the DNN (weights) at any instant of time. Therefore, l-different DNN works in parallel. A composite Lyapunov function finds the convex hull approximation of the set of DNN working together to improve the approximation capabilities of classical neural networks. The main result of this study shows the practical stability of the estimation error. Numerical simulations demonstrate the approximation capabilities of the composite DNN implemented in a Van Der Pol oscillator where the presence of high-frequency components makes difficult a classical DNN approximation.