Solving Time-Varying Vector-Valued Nonlinear Equations Including Scalar-Valued Ones As Special Cases by Gradient-Zhang Neural Net

Solving nonlinear equations plays a fundamental role in science and engineering. In this paper, gradient neural net (GNN) and Zhang neural net (ZNN), two classes of recurrent neural net, are utilized to construct a new neural net, i.e., gradient-Zhang neural net (GZNN), to solve time-varying vector-valued nonlinear equations including scalar-valued ones as special cases. Note that GNN and ZNN are proved efficient when applied in dynamic systems, such as time-varying linear equations and time-varying matrix inverses. Moreover, with the development of digital circuits, some Zhang time discretization (ZTD) formulas are presented to solve the discrete time-varying problems. In this paper, four ZTD formulas are utilized to construct discrete GZNN algorithms. Furthermore, we perform some simulation experiments to compare the performances of ZNN, GNN and GZNN, and show the feasibility of the four discrete GZNN algorithms.