Nonovershooting Prescribed Finite-Time Control for Nonlinear Pure-Feedback Systems

The paper investigates the the problem of non-overshooting tracking prescribed finite-time control for nonlinear pure-feedback systems is studied. Currently, most existing results focus on nonlinear strict-feedback systems, while studies on the more general pure-feedback systems are scarce. Moreover, the available conditions for ensuring non-overshooting performance are conservative, making it difficult to select appropriate constraints for diverse engineering applications. In this paper, we design a prescribed finite-time controller by proposing a new prescribed finite-time lemma and the backstepping technique. At the same time, a relatively simple closed-loop system is obtained. Furthermore, an analytical expression for the tracking error is derived, which facilitates the analysis of a wider range of non-overshooting conditions and thereby reduces conservatism. The proposed approach not only solves the problem of prescribed finite-time control, but also solves the problem of non-overshooting control. Finally, the simulation examples demonstrate the effectiveness of the proposed algorithm.