Adaptive tracking of stochastic nonlinear systems with Prandtl–Ishlinskii hysteresis


Wei Liu, Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027, China.



This paper deals with adaptive tracking problems for a class of stochastic nonlinear systems with unknown hysteresis nonlinearities. The system considered is in a strict-feedback form driven by unknown Prandtl–Ishlinskii hysteresis and Wiener noises of unknown covariance. By employing backstepping design techniques and stochastic Lyapunov design method, parameter adaptive laws and control laws are obtained, which ensure that the tracking error can converge to a small residual set around the origin in the sense of mean quartic value. Copyright © 2011 John Wiley & Sons, Ltd.