{'fraction_non_alphanumeric': 0.036941580756013746, 'fraction_numerical': 0.0, 'mean_word_length': 5.43646408839779, '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}}
Stepsize Range and Optimal Value for Taylor–Zhang Discretization Formula Applied to Zeroing Neurodynamics Illustrated via Future Equality-Constrained Quadratic Programming

In this brief, future equality-constrained quadratic programming (FECQP) is studied. Via a zeroing neurodynamics method, a continuous-time zeroing neurodynamics (CTZN) model is presented. By using Taylor–Zhang discretization formula to discretize the CTZN model, a Taylor–Zhang discrete-time zeroing neurodynamics (TZ-DTZN) model is presented to perform FECQP. Furthermore, we focus on the critical parameter of the TZ-DTZN model, i.e., stepsize. By theoretical analyses, we obtain an effective range of the stepsize, which guarantees the stability of the TZ-DTZN model. In addition, we further discuss the optimal value of the stepsize, which makes the TZ-DTZN model possess the optimal stability (i.e., the best stability with the fastest convergence). Finally, numerical experiments and application experiments for motion generation of a robot manipulator are conducted to verify the high precision of the TZ-DTZN model and the effective range and optimal value of the stepsize for FECQP.