Robust adaptive controls of nonlinear systems with actuator hysteresis represented by Prandtl-Ishlinskii models

The development of control techniques to mitigate the effects of unknown hysteresis preceding with plants, has recently re-attracted significant attention. This thesis deals with robust adaptive control of nonlinear systems preceded by unknown hysteresis nonlinearities. In the literature, the most common methods to reduce hysteresis effects to the controlled systems are based on the inverse hysteresis compensations. Due to the complexity of hysteresis behavior, this approach has its limit. By thoroughly investigating the Prandtl-Ishlinskii models of hysteresis, a robust adaptive control scheme was developed, which makes it possible to fuse the model of hysteresis with the available control techniques without necessarily constructing a hysteresis inverse. The global stability of the adaptive system and to track a desired trajectory to a certain precision are achieved. Two classes of nonlinear systems preceded by unknown hysteresis nonlinearities are studied. One class of systems is with parametric uncertainties and known nonlinear functions. By integrating proposed hysteresis adaptation law with sliding mode control and back-stepping techniques, the global stability and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for an example of this class of nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approaches. Then the approach is extended to a more general class of systems in the presence of parametric uncertainties and unknown nonlinear functions with bounded disturbances and preceded by unknown hysteresis nonlinearities. Combined with neural networks adaptation control method, it is proved that for any bounded initial conditions, all closed-loop signals are bounded and the state vector x ( t ) converges to a neighborhood of the desired trajectory. Concerning the practical applications, determination of the density function of the Prandtl-Ishlinskii model is crucial. In this study, a discretional approach is developed to approximate density function p ( r ) based on the memory effects of the play operator F r [ v ]( t