Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input

In this paper, adaptive neural control is investigated for a class of unknown nonlinear systems in pure-feedback form with the generalized Prandtl-Ishlinskii hysteresis input. To deal with the nonaffine problem in face of the nonsmooth characteristics of hysteresis, the mean-value theorem is applied successively, first to the functions in the pure-feedback plant, and then to the hysteresis input function. Unknown uncertainties are compensated for using the function approximation capability of neural networks. The unknown virtual control directions are dealt with by Nussbaum functions. By utilizing Lyapunov synthesis, the closed-loop control system is proved to be semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of zero. Simulation results are provided to illustrate the performance of the proposed approach.