Robust adaptive neural control for pure-feedback stochastic nonlinear systems with Prandtl-Ishlinskii hysteresis

This work considers robust adaptive neural-based control of pure-feedback stochastic nonlinear systems with the generalized Prandtl-Ishlinskii hysteresis. The mean-value theorem is employed to handle the non-affine difficulties from the generalized Prandtl-Ishlinskii hysteresis and the pure-feedback systems. By using the radial basis function (RBF) neural networks' universal approximation capability and backstepping technique, an adaptive neural control scheme with minimum adaptive parameter is developed. The presented controller can guarantee the semi-global boundedness in fourth-moment of all signals of the resulting closed-loop system. Furthermore, the system output is ensured to converge to a small domain of the given trajectories. Simulation results are presented to demonstrate the effectiveness of the scheme.