Adaptive fixed-time TSM for uncertain nonlinear dynamical system under unknown disturbance

For nonlinear systems subjected to external disturbances, an adaptive terminal sliding mode control (TSM) approach with fixed-time convergence is presented in this paper. The introduction of the fixed-time TSM with the sliding surface and the new Lemma of fixed-time stability are the main topics of discussion. The suggested approach demonstrates quick convergence, smooth and non-singular control input, and stability within a fixed time. Existing fixed-time TSM schemes are often impacted by unknown dynamics such as uncertainty and disturbances. Therefore, the proposed strategy is developed by combining the fixed-time TSM with an adaptive scheme. This adaptive method deals with an uncertain dynamic system when there are external disturbances. The stability of a closed-loop structure in a fixed-time will be shown by the findings of the Lyapunov analysis. Finally, the outcomes of the simulations are shown to evaluate and demonstrate the efficacy of the suggested method. As a result, examples with different cases are provided for a better comparison of suggested and existing control strategies.