A robust noise tolerant zeroing neural network for solving time-varying linear matrix equations

Abstract

A robust noise-tolerant zeroing neural network (ZNN) is introduced for solving time-varying linear matrix equations (TVLME). The convergence speed of designed neural dynamics is analyzed theoretically and compared with the convergence of neural networks which include traditional activation functions, such as the tunable activation function, versatile activation function, and the modified sign-bi-power activation function. The proposed activation is utilized in the development of nonlinear ZNN dynamics for solving time-varying linear matrix equations and the Stein equation. We investigate theoretically and experimentally the behavior of the proposed robust noise-tolerant ZNN with the novel effective activation function. In particular, the convergence analysis of proposed ZNN flows is studied both in the presence of noise and without noise. Simulation tests demonstrate the effectiveness and domination of the suggested activation over already existing activation functions. Further, the introduced noise-tolerant ZNN model is applied in solving the Wheatstone bridge and output tracking control problem.