Design and stability analysis for an adaptive neural network backstepping control of nonlinear system

In this paper, an adaptive neural network robust control approach is proposed for a class of SISO(single-input-single-output) nonlinear systems with completely unknown virtual control direction, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, neural network is employed to approximate the unknown parameters; a dynamic signal and nonlinear damping terms are introduced to counteract the unmodeled dynamics and dominate the nonlinear dynamic disturbances, respectively, and Nussbaum function is used to solve the unknown signs of virtual control gains. It is mathematically proved that the proposed adaptive neural robust control scheme can guarantee the uniform ultimate boundedness of the closed-loop system.