Finite-time sliding mode control for model-free nonlinear systems with adaptive disturbance bound estimation

Abstract

This paper proposes a finite-time sliding mode controller for model-free SISO nonlinear systems within the framework of model-free control. Unlike previous studies that primarily focused on asymptotic stability and required prior knowledge of the upper limit of the disturbance, the proposed method uses a power approach law to achieve finite-time convergence, while simultaneously constructing an attenuated online adaptive disturbance amplitude estimation mechanism. This eliminates the requirement for prior knowledge of the disturbance bound in controller design and avoids the phenomenon of unlimited gain. The stability of the closed-loop system is demonstrated through a non-smooth Lyapunov function, establishing practical finite-time stability conditions and ISS robustness against slowly varying disturbances. The effectiveness of the method is verified through simulations on a standard nonlinear system with strongly nonlinear dynamics and a reference signal with breakpoints. The results show that the proposed controller significantly improves convergence speed, reduces integration errors (ISE, ITAE), and limits control vibration compared to traditional MFC-iPID and SMC controllers.