Practical Predefined-Time Adaptive Tracking Control for Uncertain Nonlinear Systems With Input Saturation

Abstract

This paper investigates the practical predefined-time adaptive tracking control problem for uncertain nonlinear systems with input saturation. First, a practical predefined-time stability lemma is established, providing a theoretical basis for the controller design. Second, to eliminate the adverse effect of input saturation, a desired trajectory modification module is constructed, making the tracking mission more feasible. This scheme prevents the internal instability that traditional control schemes may encounter in the presence of input saturation. By constructing the predefined performance function and performing the coordinate transformation, it can be guaranteed that the tracking error does not exceed the constraint boundary while improving the transient performance of nonlinear systems. In addition, by combining the core function with the smooth projection operator to design the adaptive law, the non-parametric uncertainty problem is solved. Based on the predefined-time stability lemma within the framework of adaptive backstepping control method, a predefined-time adaptive tracking controller is designed. Mathematically, it is rigorously proven that the closed-loop system is practical predefined-time stable, and tracking error always evolves within the prescribed performance boundary. Finally, simulations are performed using the Micro-Electro-Mechanical System to verify theoretical findings. Note to Practitioners—Uncertain nonlinear systems are prevalent in engineering applications, such as Micro-Electro-Mechanical Systems (MEMS), industrial robotic arms, and precision manufacturing equipment. For these systems, stable tracking control confronts three key practical challenges: non-parametric uncertainties that degrade control accuracy, input saturation that triggers system internal instability, and the requirement for tracking tasks to be completed within a predefined time while satisfying error constraints. To address these challenges, this paper proposes a practical predefined-time adaptive tracking control method. Specifically, this method employs: a desired trajectory modification module to mitigate input saturation, a predefined performance function to constrain tracking errors, and an adaptive law to address non-parametric uncertainties. As the method is rigorously proven to be stable, its effectiveness is further verified through MEMS-based simulations. For practitioners working on the control of uncertain nonlinear systems, this work provides a reliable, time-constrained solution that bridges the gap between theoretical control design and real-world engineering requirements.