ZNN Continuous Model and Discrete Algorithm for Temporally Variant Optimization with Nonlinear Equation Constraints Via Novel TD Formula

For dealing with the temporally variant optimization with nonlinear equation constraints (TVONECs), a novel Zhang neural net (ZNN) model is proposed in this work. Two continuous-time computer numerical simulations are constructed to testify the feasibility and correctness of the continuous-time ZNN (CZNN) model. To facilitate the implementation of numerical algorithms on computer, a novel 11-instant time discretization (TD) formula is proposed in this article, and a discrete-time ZNN (DZNN) algorithm (i.e., 11-instant DZNN algorithm) is thus obtained. Besides, theoretical analyses prove the superiority as well as the feasibility of the DZNN11I algorithm. For comparison, other three TD formulas and corresponding discrete-time algorithms (i.e., 2-instant DZNN, 3-instant DZNN, and 7-instant DZNN algorithms) are presented. Finally, numerical experiments and an application to Kinova Jaco2 manipulator control are conducted to illustrate the superiority of the proposed model and algorithm.