A Noise-Suppressing Neural Algorithm for Solving the Time-Varying System of Linear Equations: A Control-Based Approach

It has been found that there exists an essential similarity between solving equations and controlling dynamic systems: Both errors are expected to decrease to zero (or an acceptably tiny value) as soon as possible. By exploiting such a similarity, researchers have presented and investigated continuous-time recurrent neural network models for solving time-varying problems. To be compatible with digital computers, it is desirable to develop discrete-time neural algorithms from the control perspective for performance improvement. In this paper, a discrete-time zeroing neural algorithm is proposed for the solving system of linear equations with the aid of control techniques. To lay a basis for theoretical analyses, the proposed zeroing neural algorithm with nonlinearity is converted into a second-order linear system plus a residual term, and then, analyzed using the control theory. Theoretical results and numerical experiments are provided, which illustrate that the proposed neural algorithm possesses an improved performance compared to the existing solutions.