Discrete gradient-zeroing neural network algorithms for handling future quadratic program as well as robot arm via ten-instant formula

The quadratic program, as a fundamental mathematical technique tool, plays a crucial role in applied mathematics and control engineering fields. With the aid of a ten-instant discrete formula processing the precision of order-6, two ten-instant-type discrete gradient-zeroing neural network algorithms that are developed from continuous gradient-zeroing neural network models are proposed to solve the problem of the future quadratic program subject to linear equation constraint with unknown futureness information. The convergence properties of continuous gradient-zeroing neural network models for solving the time dependent quadratic program problem subject to linear equation constraint are proved by Lyapunov stability theory, while the error pattern properties of ten-instant-type discrete gradient-zeroing neural network algorithms for solving the future quadratic program problem subject to linear equation constraint are studied using the stability theory of the multi-step method. Moreover, two numerical experiments are conducted to show the effectiveness and high precision of the proposed ten-instant-type discrete gradient zeroing neural network algorithms. In the end, comparison simulations for solving the path-tracking problem of the PUMA560 robot arm are further performed to substantiate the applicability, validity, and superiority of the proposed ten-instant-type discrete gradient-zeroing neural network algorithms.(c) 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.