Solution to Asymptotic Stability in Tracking Control of Nonlinear Systems With Control Input Differentiation, Actuator Dynamics, and Saturation Constraints

ABSTRACT The design of stable high‐performance precision controllers is often confronted with a set of actuation input nonlinearities and dynamical systems where the control input's time derivative appears as an inherent higher order dynamics term in the governing physical equations. This paper presents a permanently feasible asymptotically stable control architecture that addresses mathematical intricacies of this class of systems, designed to ensure robust stability and precise trajectory tracking despite parametric uncertainty and measurement noise, as well as concurrent imposition of multiple, cascaded saturation input nonlinearities within the main system and actuator. Built upon a gradient descent (GD)‐optimised dual‐mode discrete sliding‐mode control, the proposed framework systematically addresses these complexities through an advanced trajectory modification scheme, which defines the feasible operating region by computing the intersection of multiple constraint‐derived sets. The result is a control methodology that provides solid performance for systems where actuator dynamics, constraints, and input derivative terms emerge as intrinsic non‐negligible features. The algorithm also deeply mitigates the dependence on parameter pre‐tuning while offering low computational burden, as substantiated by dedicative analyses. It further utilises optimal position–velocity mode synergy for smooth tracking of even high‐frequency or discontinuous reference trajectories. Simulation results and subsequent comparisons verify the effectiveness of the control algorithm in terms of tracking accuracy, lower energy consumption, and enhanced robustness against parameter uncertainty. To validate real‐time performance compatibility, the controller was implemented on an isolated 2.8 GHz Intel Core i7 core under the EVL real‐time Linux kernel. During a 30‐s run at a 100 Hz sample rate, it exhibited a 2.66‐ms average execution time and a 5.54‐ms maximum (well under the 10‐ms allotted period) with no missed deadlines despite the presence of execution time jitter and statistical outliers. The sustained throughput of 393.16 Hz demonstrates that the proposed controller achieves both an affordable computational burden and deterministic timing suitable for embedded applications.