ZFD Formula 4igsfd_y Applied to Future Minimization

In this paper, a 4-instant g-square finite difference formula with subtype Y [termed Zhang finite difference (ZFD) formula 4IgSFD_Y] with analysis and application for future minimization (i.e., discrete-time varying minimization) is proposed and investigated, where g denotes the sampling gap. At first, a continuous-time zeroing neural network (ZNN) model is presented for continuous-time varying minimization. The proposed ZFD formula 4IgSFD_Y effectively approximates the 1st-order derivative in computation, and a discrete-time ZNN model is obtained by adopting the ZFD formula 4IgSFD_Y to discretize the continuous-time ZNN model. For comparison, Newton iteration for the future minimization is also presented in this paper. In addition, the discrete-time ZNN model with O(g3) residual error pattern performs more accurately than the Newton iteration with O(g) residual error pattern. Finally, illustrative numerical experiments are conducted and analyzed to show the efficacy and superiority of the discrete-time ZNN model for the future minimization.