{'fraction_non_alphanumeric': 0.016800584368151936, 'fraction_numerical': 0.0, 'mean_word_length': 5.782178217821782, '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}}
Smooth Neuroadaptive PI Tracking Control of Nonlinear Systems With Unknown and Nonsmooth Actuation Characteristics

This paper considers the tracking control problem for a class of multi-input multi-output nonlinear systems subject to unknown actuation characteristics and external disturbances. Neuroadaptive proportional–integral (PI) control with self-tuning gains is proposed, which is structurally simple and computationally inexpensive. Different from traditional PI control, the proposed one is able to online adjust its PI gains using stability-guaranteed analytic algorithms without involving manual tuning or trial and error process. It is shown that the proposed neuroadaptive PI control is continuous and smooth everywhere and ensures the uniformly ultimately boundedness of all the signals of the closed-loop system. Furthermore, the crucial compact set precondition for a neural network (NN) to function properly is guaranteed with the barrier Lyapunov function, allowing the NN unit to play its learning/approximating role during the entire system operation. The salient feature also lies in its low complexity in computation and effectiveness in dealing with modeling uncertainties and nonlinearities. Both square and nonsquare nonlinear systems are addressed. The benefits and the feasibility of the developed control are also confirmed by simulations.