Adaptive Predefined‐Time Stabilization for A Class of Nonlinear Time‐Delay Systems With Input Unmodeled Dynamics

ABSTRACT In this paper, a predefined‐time control scheme, which intends to stabilize the concerned nonlinear time‐delay systems possessing input unmodeled dynamics, is developed. During the controller design procedure, a predefined‐time controller exported by following the backstepping technique is applied to the stabilizer of such concerned system, and the Lyapunov‐Krasovskii functionals (LKFs), M‐filter are respectively introduced to deal with the time delays and input unmodeled dynamics. Meanwhile, the fractional power piecewise function is constructed in the stabilizer to avoid the singularity problem caused by differentiating the virtual control laws at the origin. In addition, the neural networks are introduced to deal with the apparent nonlinearities by basing on their approximation ability. In stability analysis, under the proper selection of Lyapunov function candidates(LFC), we can verify that all signals in the formulating closed‐loop system can possess the property of semi‐global uniformly ultimately bounded (SGUUB) within a given predefined‐time, and simulations, which cover theoretical and practical simulations, can reflect the availability of the developed scheme.