{'fraction_non_alphanumeric': 0.013930348258706468, 'fraction_numerical': 0.0, 'mean_word_length': 5.448717948717949, '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 output feedback boundary control for a class of axially moving system

In this study, the main concern lies in the development of a boundary control scheme for suppressing the vibration of an axially moving system under the influence of unknown disturbances. To that end, a boundary adaptive output feedback control is presented by merging Lyapunov theory, observer backstepping technique, high-gain observers and robust adaptive control theory to globally stabilise the vibration and compensate for the uncertainties of the system. Besides, the disturbance observer dynamics is developed to handle unknown boundary disturbance and the σ -modification is adopted to adjust the robustness of the system. Under the designed control, the uniformly bounded stability of the controlled system is achieved, and the state observer error exponentially converges to zero as time tends to infinity. Simulation results illustrate that the proposed control can stabilise the system with a better performance.