Predefined-Time Precise Tracking of Uncertain MIMO Nonlinear Systems With Time-Varying Input Delay

This paper investigates the adaptive predefined-time (PT) precise tracking control for uncertain nonlinear multi-input multi-output (MIMO) systems with time-varying input delay. Precise tracking in uncertain MIMO nonlinear systems is particularly challenging, especially when uncertainties include unknown control directions, nonlinear functions, and external disturbances. This paper extends the existing methods that typically require specific controllability conditions by proposing a novel PT precise tracking control scheme for more general MIMO strict-feedback nonlinear systems. This approach introduces an L-K functional containing positive definite time-varying function matrices, combines bounded estimation techniques with the backstepping method, and incorporates auxiliary signals to compensate for the effects of time-varying input delay. The proposed scheme ensures the boundedness of all closed-loop system signals and provides a rigorous proof that the auxiliary signals are also bounded, while guaranteeing that the tracking error converges to origin within the predefined time. Finally, the proposed PT control scheme is verified by two numerical simulation examples.