Adaptive tracking control for nonlinear system in pure-feedback form with prescribed performance and unknown hysteresis

The finite-time tracking control issue for a class of nonlinear pure-feedback system with prescribed performance and unknown hysteresis is investigated in this work. To solve the Bouc-Wen hysteresis with unknown parameters and direction conditions, the Nussbaum function and auxiliary virtual control function are used. A finite-time performance function is applied in prescribed performance, which can make the tracking error is limited to a pre-given boundary in finite time. Moreover, the mean-value theorem is applied to solve the difficulty of pure-feedback form. Combined with backstepping technique, an adaptive tracking control scheme is designed to make sure that all the closed-loop signals are bounded and that the tracking error converges to pro-given boundary. Finally, a simulation example is presented to show the effectiveness of the proposed control scheme.