Direct adaptive neural control of nonlinear strict-feedback systems with unmodeled dynamics using small-gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single-input and single-output strict-feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict-feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme.