Solving time-varying linear inequalities by finite-time convergent zeroing neural networks

Abstract

In this paper, to solve time-varying linear inequalities much faster, on basis of zeroing neural network (ZNN), two finite-time convergent ZNN (FTCZNN) models are proposed by exploiting two novel nonlinear activation functions (AFs). The first FTCZNN model is established by using the sign-bi-power AF which is termed as FTCZNN-S for presentation convenience. The second one is established by amending the sign-bi-power AF through adding a linear term, and called FTCZNN-SL. Compared with existing ZNN models for time-varying linear inequalities, the proposed two FTCZNN models possess prominent finite-time convergence performance. In addition, theoretical analysis is given to estimate the finite-time convergence upper bounds of those two FTCZNN models. Numerical comparative results ulteriorly validate the effectiveness and dominance of two FTCZNN models for finding the solution of time-varying linear inequalities.