Learning-Based Robust Fixed-Time Terminal Sliding Mode Control

In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The first theorem addresses the fully known system model, while the second considers situations where the system's drift is approximated utilizing Gaussian processes (GP) for approximating unknown dynamics. Both theorems establish the global fixed-time stability of the closed-loop system. The stability analysis is based on a straightforward quadratic Lyapunov function. Our proposed method outperforms an established adaptive fixed-time sliding mode control approach, especially when ample training data is available.