A Class Of Sampled Nonlinear Systems With Hysteresis Characteristics And Their Control

The common factors existed in various practical systems,such as hysteresis,uncertainty,and external disturbances have a great impact on the performance of the system.To our knowledge,a lot of results have been achieved in the control research of nonlinear systems with hysteresis characteristics,while most of the researching results are based on continuous hypothesis and few results are derived based on sampling control theory.Moreover,the theory of sampling control has attracted the attention of many scholars with the rapid development of computer technology.Therefore,it is necessary to investigate the sampled-date nonlinear system with hysteresis characteristics.Furthermore,this paper discusses the control problems of a class of nonlinear sampling systems with hysteresis characteristics based on sampling control theory,Lyapunov stability theory,adaptive control,disturbance compensation control and other theories and control methods.The main research contents of this paper are as follows:(1)Prandtl-Ishlinskii and Backlash-like hysteresis models are investigated,where the Prandtl-Ishlinskii hysteresis model is selected as the input of the nonlinear sampling system in this paper.Besides,we employ radial basis function(RBF)neural network to approximate the unknown nonlinear part decomposed by hysteresis.At the same time,we further relax the limitation of non-zero constant control gain parameter by the approximation of the hysteresis loop,and reduce the error range of the system.(2)For a class of uncertain nonlinear system with unknown Prandtl-Ishlinskii hysteresis input,a design scheme of adaptive sampled-data observer and adaptive output feedback controller based on RBF neural network is proposed.Considering the sampling output,the adaptive sampling observer and adaptive output feedback controller are designed by using the excellent approximation ability of RBF neural networks.Besides,the entire closed-loop system is proved to be uniformly ultimately bounded based on the established sampled nonlinear systems uniformly ultimately bounded sufficient conditions and the constructed LyapunovKrasovskii functional.The satisfactory control performance of the system is guaranteed under the condition of unknown hysteresis input and unmeasured states.(3)Based on the above research,we propose a design scheme of anti-disturbance adaptive sampled-data observer and anti-disturbance adaptive output feedback controller based on RBF neural network and disturbance estimator for uncertain nonlinear systems with unknown Prandtl-Ishlinskii hysteresis input and external disturbances.Meanwhile,we solve the parameter selection problem based on the disturbance compensation control method that estimates the compound disturbance in the system through the designed disturbance estimator.The uniformly ultimately bounded of all closed-loop signals are guaranteed under the condition of unknown hysteresis input,unknown external disturbances and unmeasured states.