Discrete time-variant nonlinear optimization and system solving via integral-type error function and twice ZND formula with noises suppressed

In this paper, by using integral-type error function and twice zeroing neural-dynamics (or termed, Zhang neural-dynamics, ZND) formula, continuous-time advanced zeroing neural-dynamics (CT-AZND) model is proposed for solving the continuous time-variant nonlinear optimization problem. Furthermore, a discrete-time advanced zeroing neural-dynamics (DT-AZND) model is first proposed, analyzed, and investigated for solving the discrete time-variant nonlinear optimization (DTVNO) problem. Theoretical analyses show that the proposed DT-AZND model is convergent, and its steady-state residual error has an \(O(g^3)\) pattern with g denoting the sampling gap. In addition, in the presence of various kinds of noises, the proposed DT-AZND model possesses advantaged performance. In detail, the proposed DT-AZND model converges toward the time-variant theoretical solution of the DTVNO problem with \(O(g^3)\) residual error in the presence of an arbitrary constant noise and has excellent ability to suppress linear-form time-variant noise and bounded random noise. Illustrative numerical experiments further substantiate the efficacy and advantage of the proposed DT-AZND model for solving the DTVNO problem.