RNN for Solving Perturbed Time-Varying Underdetermined Linear System With Double Bound Limits on Residual Errors and State Variables

Abstract

Neural networks have been generally deemed as important tools to handle kinds of online computing problems in recent decades, which have plenty of applications in science and electronics fields. This paper proposes a novel recurrent neural network (RNN) to handle the perturbed time-varying underdetermined linear system with double bound limits on residual errors and state variables. Beyond that, the bound-limited underdetermined linear system is converted into a time-varying system that consists of linear and nonlinear formulas through constructing a nonnegative time-varying variable. Then, theoretical analyses are conducted to verify the superior convergence performance of the proposed RNN model. Furthermore, numerical experiment results and computer simulations demonstrate the superiority and effectiveness of the proposed RNN model for handling the time-varying underdetermined linear system with double bound limits. Finally, the proposed RNN model is applied to the physically limited PUMA560 robot to show its satisfactory applicabilities.