New Recurrent Neural Network for Online Solution of Time-Dependent Underdetermined Linear System With Bound Constraint

Abstract

Recurrent neural network (RNN) has recently been viewed as a significant alternative to online mathematical problem solving. This paper offers important improvements by proposing the first RNN model to solve the time-dependent underdetermined linear system with bound constraint. In particular, by introducing a time-dependent nonnegative vector, the bound-constrained underdetermined linear system is initially transformed into a time-dependent system that comprises linear and nonlinear equations. The newly constructed RNN model can thus zero in on the time-dependent equations. Then, the model is theoretically proven to have convergence properties, and the simulation results further substantiate the efficacy of the proposed RNN model to solve the time-dependent underdetermined linear system with bound constraint. Finally, the proposed RNN model is applied to physically constrained redundant robot manipulators, thereby indicating the applicability of the proposed model.