A novel dynamic signal Lemma for predefined-time stabilization of high-order nonlinear systems with dynamic uncertainties.

This research considers the problem of predefined-time adaptive neural control for high-order nonlinear systems with dynamics uncertainties. Through the application of neural networks, the unknown nonlinear functions of the systems are approximated. In order to avoid the "complexity explosion problem", a novel predefined-time dynamics surface is designed for high-order nonlinear systems. Regarding the dynamics uncertainties existing within the systems, this paper designs and introduces a modified predefined-time dynamics signal to address the aforementioned issue. By using a backstepping design scheme, the neural predefined-time control approach is proposed so that all signals in considered systems are bounded within a predefined time. To verify the validity of the proposed method, an illustrative example is presented.