New Discrete-Time Models of Zeroing Neural Network Solving Systems of Time-Variant Linear and Nonlinear Inequalities

In this paper, a new one-step-ahead numerical differentiation rule termed 5-instant discretization formula is proposed for the first-order derivative approximation with higher computational precision. Then, by exploiting the proposed formula to discretize the continuous-time zeroing neural network [or termed, continuous-time Zhang neural network (ZNN)] models, two new discrete-time zeroing neural network [or termed, discrete-time ZNN (DTZNN)] models are proposed, analyzed and investigated for solving systems of discrete time-variant inequalities, including the system of discrete time-variant linear inequalities and the system of discrete time-variant nonlinear inequalities. For comparative purposes, the recently developed Taylor-type DTZNN models and the widely used Euler-type DTZNN models are also presented. Theoretical analyses show that the proposed DTZNN models are convergent, and their steady-state residual errors have an <inline-formula> <tex-math notation="LaTeX">$O(g^{4})$ </tex-math></inline-formula> pattern with <inline-formula> <tex-math notation="LaTeX">$g$ </tex-math></inline-formula> denoting the sampling gap. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed DTZNN models for solving the systems of discrete time-variant inequalities.