Adaptive Prescribed-Time Filtered Control Design for a Full-State Constrained Nonlinear System

In this article, an adaptive prescribed-time neural controller is developed for the tracking problem of a class of high-order nonlinear systems with full-state constraints. First, a prescribed-time bounded stability criterion is designed. Then, to handle the "explosion of complexity" problem of the backstepping method, an adaptive prescribed-time filter is constructed, in which the filter error is prescribed-time stable. Compared with existing methods, the newly designed transformation approach can accommodate a broader range of state constraint types. Then, the unknown nonlinear function is handled by radial basis function neural networks (RBFNNs). The adaptive prescribed-time neural control scheme is developed based on above. It can guarantee that the closed-loop system achieves the prescribed-time stability, and all states do not transgress the constraints. To demonstrate the effectiveness of the control strategy, comparative simulations are provided at the end.