{'fraction_non_alphanumeric': 0.019251336898395723, 'fraction_numerical': 0.0, 'mean_word_length': 5.324324324324325, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Adaptive finite‐time tracking control for time‐varying output constrained non‐linear systems with unmatched uncertainties

In this study, an adaptive finite-time tracking control for a class of output constrained non-linear systems is studied. Both parametric uncertainty and external disturbance of the system are considered. Using a novel adaptive backstepping control scheme with a tuning function, a robust controller is obtained. It drives the tracking error to converge to a small neighbourhood of origin in finite time in spite of the unmatched uncertainties. Except for the finite-time convergence, it is also proved that the whole closed-loop signals are bounded and the system output is constrained within the predefined open set for all the system running time. Finally, two examples which includes one numerical example and one single-link robot are provided to demonstrate the effectiveness of the proposed control scheme.