Prescribed-Time High-Order Sliding Mode Control Subject to Mismatched Terms With Unknown Gain Functions

This study presents a novel prescribed-time high-order sliding mode (HOSM) controller for uncertain nonlinear systems. First, a new sliding mode dynamic system with mismatched terms is constructed. In contrast to existing HOSM algorithms, the proposed approach relaxes the assumption of gain functions imposed on the growth condition of the mismatched terms, allowing them to be unknown. Second, a novel prescribed-time HOSM controller is designed for the new sliding mode dynamic system using the concept of time-varying scaling function. Lyapunov analysis demonstrates that the proposed controller guarantees the convergence of the sliding variables to zero within a prescribed time, irrespective of the initial conditions of the system and other control parameters. Finally, simulation comparisons are provided to verify the theoretical results.