Adaptive Prescribed-Time Neural Control of Nonlinear Systems via Dynamic Surface Technique

The adaptive practical prescribed-time (PPT) neural control is studied for multiinput multioutput (MIMO) nonlinear systems with unknown nonlinear functions and unknown input gain matrices. Unlike existing PPT design schemes based on backstepping, this study proposes a novel PPT control framework using the dynamic surface control (DSC) approach. First, a novel nonlinear filter (NLF) with an adaptive parameter estimator and a piecewise function is constructed to effectively compensate for filter errors and facilitate prescribed-time convergence. Based on this, a unified DSC-based adaptive PPT control algorithm, augmented with a neural networks (NNs) approximator, is developed, where NNs are used to approximate unknown nonlinear system functions. This algorithm not only addresses the inherent computational complexity explosion associated with traditional backstepping methods but also reduces the constraints on filter design parameters compared to the DSC algorithm that relies on linear filters. The simulation showcases the effectiveness and superiority of the devised scheme by employing a two-degree-of-freedom robot manipulator.