Abstract
In this paper, a six-point discretization (6PD) formula is presented to discretize continuous-time models. Then, by using the 6PD formula and introducing the adaptivity/variability of parameter, a new-type discrete-time gradient (DTG) model is proposed to solve a discrete dynamic nonlinear equation system (DDNES) with occasionally-singular Jacobian matrix. For comparative purposes, based on the 6PD formula, a 6PD-type discrete-time zeroing (DTZ) model and an old-type (i.e., conventional) DTG model are also presented to handle the same problem. Finally, comparative numerical experiments, including an application to the discrete-time motion control of a robot manipulator, are conducted to substantiate the validity and superiority of the new-type DTG model for solving the DDNES with occasionally-singular Jacobian matrix. That is, when the Jacobian matrix of DDNES occasionally becomes singular as time evolves, the new-type DTG model can provide a feasible and effective solution to the singular Jacobian problem, whereas the other presented models fail to achieve such a solution.
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