Adaptive control of a class of strict-feedback discrete-time nonlinear systems with unknown control gains and preceded by hysteresis

In this paper, adaptive control is studied for a class of discrete-time nonlinear systems in strict-feedback form. The systems are with unknown control gains and are proceeded by hysteresis. Prandtl-Ishlinskii (PI) model is used to describe the hysteresis. The control design is based on the predicted future states and discrete Nussbaum gain is employed in the parameter update law to deal with the unknown control directions. All the closed-loop signals are guaranteed to be bounded and the output tracking error is made to be within a neighborhood around zero ultimately. The effectiveness of the proposed control law is demonstrated in the simulation.