Direct adaptive regulation of unknown nonlinear dynamical systems via dynamic neural networks

A direct nonlinear adaptive state regulator, for unknown dynamical systems that are modeled by dynamic neural networks is discussed. In the ideal case of complete model matching, 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 dynamic neural network model in the sence that it is of higher order, or due to the presence of a modeling error term. In both cases, modifications of the original control and update laws are provided, so that at least uniform ultimate boundedness is guaranteed, even though in some cases the stability results obtained for the ideal case are retained.