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Abstract

Finite/fixed-time control provides a valuable approach for optimizing a system’s settling time; however, it lacks the flexibility to independently define both the settling time and the convergence domain. Unlike traditional approaches that address semi-global bounded tracking for pure feedback systems, this paper achieves not only convergence of tracking errors to zero but also ensures that the convergence time can be predefined according to user requirements. To develop the desired predefined-time controller, a mild semi-bounded assumption for non-affine functions is first introduced, which addresses the design challenges posed by pure feedback structures. Then, by leveraging the properties of Radial Basis Function (RBF) neural networks and Young’s inequality, an upper bound for unknown nonlinear functions and external disturbances is derived. Finally, a predefined-time virtual control input is provided, and its derivative is estimated using a finite-time differentiator. It is rigorously proven that the proposed novel predefined-time controller guarantees global convergence of tracking errors to zero within the specified time. The effectiveness and practicality of this predefined-time control method are validated through examples.