Adaptive neural network output feedback control for a class of non-affine non-linear systems with unmodelled dynamics

In this study, an output feedback-based adaptive neural controller is presented for a class of uncertain non-affine pure-feedback non-linear systems with unmodelled dynamics. Two major technical difficulties for this class of systems lie in: (i) the few choices of mathematical tools in handling the non-affine appearance of control in the systems, and (ii) the unknown control direction embedded in the unknown control gain functions, in great contrast to the standard assumptions of constants or bounded time-varying coefficients. By exploring the new properties of Nussbaum gain functions, stable adaptive neural network control is possible for this class of systems by using a strictly positive-realness-based filter design. The closed-loop system is proven to be semi-globally uniformly ultimately bounded, and the regulation error converges to a small neighbourhood of the origin. The effectiveness of the proposed design is verified by simulations.