This paper investigates the adaptive finite-time tracking control problem for a class of switched nonlinear systems with unmodeled dynamics. In practical applications, switched systems usually possess unfavourable factors, such as unmeasured states and unmodeled dynamics both of which are taken into account in this paper. A dynamic signal defined with a special property is introduced in this paper to improve control performance while garanteeing stability of the controlled system. By designing an observer, a finite-time adaptive output-feedback tracking controller is constructed via the backstepping technique. Then, the finite-time stability problem of the considered systems is studied. It is shown that all the signals in the closed-loop system are semi-globally uniformly finite-time bounded (SGFUB), and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. It is noted that, the design process is less complex than some existing results on tackling control problems of nonlinear systems with unmodeled dynamics. In the example, the simulation result testifies the effectiveness of the proposed method.

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.