This paper proposes an adaptive non-singular fast terminal sliding mode control (FTSMC) with integral surface for the finite time tracking control of nonlinear systems with external disturbances. An appropriate parameter-tuning adaptation law is derived to tackle the disturbances. A new fast terminal sliding scheme with self-tuning algorithm is proposed to synthesize the adaptive non-singular fast integral terminal sliding approach. The proposed approach has the following features: 1) It does

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... t require the derivative of the fractional power terms with respect to time, thereby eschewing the singularity problem typically associated with TSMC; 2) It guarantees the existence of the switching phase under exogenous disturbances with unknown bounds; 3) Because of the integral terms in the sliding surface, the power functions are hidden behind the integrator; 4) It ensures chattering-free dynamics. The effectiveness of the proposed approach is assessed using both a simulation and an experimental study. The obtained results showed that the FTSM control technique guarantees that when the switching surface is reached, tracking errors converge to zero at a fast convergence rate. Additionally, the integral term offers one extra degree-of-freedom and since the time-derivative of fractional power terms is not needed in the controller, the proposed switching surface provides a comprehensive framework for singularity avoidance. INDEX TERMS Non-singular control, sliding mode control, integral sliding surface, adaptive control, nonlinear system.