In previous works, a learning law with a dead zone function was developed for multilayer differential neural networks. This scheme requires strictly a priori knowledge of an upper bound for the unmodeled dynamics. In this paper, the learning law is modified in such a way that this condition is relaxed. By this modification, the tuning process is simpler and the dead-zone function is not required anymore. On the basis of this modification and by using a Lyapunov-like analysis, a stronger result is here demonstrated: the exponential convergence of the identification error to a bounded zone. Besides, a value for upper bound of such zone is provided. The workability of this approach is tested by a simulation example.
J. Humberto Pérez-Cruz. A. Y. Alanis. José de Jesús Rubio. Jaime Pacheco. "System Identification Using Multilayer Differential Neural Networks: A New Result." J. Appl. Math. 2012 1 - 20, 2012. https://doi.org/10.1155/2012/529176