Predefined‐Time Prescribed Performance Adaptive Tracking Control for Nonlinear Systems Relaxing Feasibility Condition

ABSTRACT

This study addresses the tracking control issue for unknown nonlinear systems, focusing on predefined‐time prescribed performance. The core contribution lies in establishing a unified control framework that integrates deferred prescribed performance with predefined‐time stability, yielding a dual‐time guarantee that transforms the convergence process from asymptotic behavior to a scheduled task with a user‐defined time. The deferred prescribed performance method ensures that the system error converges from any initial state, while the predefined‐time controller guarantees rigorous convergence within the prescribed duration. By employing a smooth shifting function and dynamic scaling, the constrained issue is reformulated into an unconstrained form, thus removing the feasibility condition on initial state restrictions. It further compensates for system uncertainties through neural network adaptation. The Lyapunov‐based analysis verifies the boundedness of all closed‐loop signals, predefined‐time convergence of the tracking error, and preservation of the prescribed transient and steady‐state performance. Compared to existing methods, the proposed strategy significantly improves practicality and robustness while maintaining guaranteed convergence speed and control accuracy. Finally, simulation studies are carried out to validate the effectiveness of the proposed control strategy.