Improved zeroing neural networks for finite time solving nonlinear equations

Nonlinear equation is an important cornerstone of nonlinear science, and many practical problems in scientific and engineering fields can be described by nonlinear equation in mathematics. In this paper, improved zeroing neural network (IZNN) models are presented and investigated for finding the solutions of the time-invariant nonlinear equation (TINE) and time-varying nonlinear equation (TVNE) in predictable and finite time. Compared with the exponential convergence zeroing neural network (ZNN), the convergence time of the IZNN models is finite and able to be estimated; in addition, the IZNN model is more stable and reliable for solving high-order TVNE. Both of the theoretical and numerical simulation results of the ZNN and IZNN for finding the solutions of the TINE and TVNE are presented to demonstrate the superiority and effectiveness of the IZNN model.