Adaptive finite‐time tracking control of uncertain non‐linear n ‐order systems with unmatched uncertainties

This study focuses on the adaptive finite-time tracking problem for uncertain non-linear n-order systems subjected to unmatched uncertainties. Using a novel form of fast terminal sliding mode (FTSM) control method with self-tuning algorithm, a robust controller is obtained to drive the tracking error to origin in finite time in spite of the unmatched uncertainties. Indeed, the adaptive FTSM is combined with a global SMC approach to eliminate the reaching phase which improves the performance and robustness of the system. To alleviate chattering phenomenon and get rid of knowing the exact value of upper bound of the uncertainties, a bipolar sigmoid function with adjustable gains is presented to replace signum function. The Lyapunov stability theory is utilised to establish the stability and robustness features of the suggested law. The proposed controller provides an appropriate performance as well as finite-time convergence of tracking error to zero and this issue is verified through simulation results.