Robust Adaptive Fixed-Time Terminal Sliding Mode Control with Disturbance Observer for Nonlinear Systems

Abstract

This paper proposes a robust and efficient control strategy for a class of second-order uncertain nonlinear systems by integrating Adaptive Fixed-Time Terminal Sliding Mode Control (AFTSMC) with a low-pass filtered Disturbance Observer (DO), forming the novel AFTSMC-DO framework. The proposed approach addresses key challenges in nonlinear system control: fast convergence, chattering mitigation, and disturbance rejection. The AFTSMC design leverages a non-singular fast terminal sliding manifold, ensuring that system trajectories converge to the desired reference in a fixed time independent of initial conditions. To further improve disturbance rejection and reduce reliance on high control gains, a DO is introduced to estimate unknown matched disturbances using filtered state derivatives, enhancing both transient performance and robustness. A rigorous Lyapunov-based analysis proves the global fixed-time stability of both the tracking errors and disturbance estimation error. The disturbance bound is adaptively estimated using a barrier Lyapunov function (BLF), ensuring bounded and smooth adaptation. Theoretical guarantees are supported by a comprehensive comparative simulation on the inverted pendulum on a cart-a classic benchmark of underactuated nonlinear dynamics. The proposed AFTSMC-DO is compared with the Adaptive Full-Order Time-Varying Sliding Mode Control (AFOTVSMC). Simulation results show that AFTSMC-DO achieves faster convergence, lower steady-state error, better tracking under time-varying disturbances, and lower control effort. These advantages make AFTSMC-DO a promising candidate for applications in robotics, aerospace, and industrial systems requiring rapid and robust control under uncertainty.