Dynamic Predefined‐Time Prescribed Performance Sliding Mode Control for MIMO Underactuated Systems With Mismatched Disturbances

We develop an output‐feedback control scheme with a dynamic predefined‐time performance envelope for a class of multi‐input underactuated systems that satisfy specified rank and coupling conditions. Known disturbance internal models are embedded in a generalized disturbance estimator (GDE), which also reconstructs an unknown component with bounded rate. Explicit estimation error bounds provide the margins needed to compute adaptive boundary updates of finite magnitude using the estimated task errors. Coupled tasks are regulated through sliding mode control with exact null‐space allocation. Under stated observability, initialization, and actuator conditions, a regional analysis establishes bounded closed‐loop states, practical tracking bounds, and feasibility of the physical error envelopes. If no reset occurs during a complete contraction interval, the actual task errors satisfy the terminal performance bounds at the prescribed deadline. Conditions are derived to prevent resets from accumulating in finite time and to ensure that resetting eventually ceases. Separate bounds are obtained on the times for the observer and task errors to enter their respective residual sets. Buck‐converter simulations show faster voltage recovery at the cost of larger duty‐ratio excursions, while a planar vertical takeoff and landing (PVTOL) example demonstrates improved estimation and selective resetting with comparable task‐tracking performance.