Direct adaptive regulation using recurrent neural networks: the case of unmodeled dynamics

A direct nonlinear adaptive state regulator, for unknown dynamical systems that are modeled by recurrent neural networks is discussed. In an ideal case of complete model matching, the convergence of the state to zero plus boundedness of all signals in the closed loop is ensured. Moreover, the behavior of the closed loop system is analyzed for cases in which the true plant differs from the recurrent neural network model in the sense that it is of higher older, that was originally assumed. Modifications of the original control and update laws are provided, so that at least uniform ultimate boundedness is guaranteed