Nonlinear adaptive control in the presence of unmodelled dynamics using neural networks

We discuss the tracking problem in the presence of unmodelled dynamics, for affine in the control nonlinear dynamical systems, whose nonlinearities are assumed unknown, using recurrent neural network structures. Based upon their proven approximation capabilities, Lyapunov stability theory is employed to develop smooth, partial state control and update laws, to guarantee the uniform ultimate boundedness of the tracking error, as well as uniform boundedness of all other signals in the closed loop. The above are achieved without the a priori knowledge of upper bounds on the norms of the optimal weight values. For the unmodelled dynamics, an input-to-output practically stable and unboundedness observability assumptions are necessary.