Adaptive Practical Predefined-Time Control for Nonlinear Strict-Feedback Systems via Smooth Command Filters

Abstract

This paper develops a practical predefined-time control framework for nonlinear systems subject to bounded disturbances and derives an explicit relationship between the settling-time upper bound and the scaling factor, providing a generalization of existing predefined-time stability results. By employing a reciprocal-quadratic integration technique, new sufficient conditions are established to ensure that the system states converge to a bounded residual set within a predefined time. Furthermore, a key inequality is developed to support controller design, smooth command-filtered backstepping implementation, and parameter adaptation, thereby enabling the implementation of smooth adaptive practical predefined-time control. Numerical simulations demonstrate that practical stabilization is achieved within the prescribed time and that convergence performance can be flexibly tuned via parameter selection. Note to Practitioners—This work is motivated by tracking problems in automated motion-control systems, including robotic manipulators, servo mechanisms, and autonomous vehicles, where predictable response times are often required rather than merely asymptotic convergence. In practical applications, initial conditions may be uncertain, external disturbances are inevitable, and repeated differentiation operations in backstepping designs can increase implementation complexity. Although finite-time and fixed-time control methods can accelerate convergence, their settling-time specifications are not always straightforward to tune and may result in conservative controller designs. To address these limitations, this paper develops a practical predefined-time tracking framework that allows the designer to explicitly assign the desired upper bound of the convergence time. Smooth command filters are introduced to reduce implementation complexity, while an adaptive mechanism enhances robustness against model uncertainties and external disturbances. The proposed controller provides a practical solution for automation systems that require fast, adjustable, and robust tracking performance. Simulation studies on a robotic manipulator verify its effectiveness, and future research will investigate experimental implementation and validation.