Power-sum Function Activated Recurrent Neural Network Model for Solving Multi-linear Systems with Nonsingular M-tensor

Recurrent neural network (RNN), as a branch of artificial intelligence, shows powerful abilities to solve the complicated computational problems. Due to the similarity between solving equations and controlling dynamic systems, RNN-based approaches can also be analysed from the perspectives of control. Multi-linear systems, on the other hand, are a type of tensor equations with considerable complexity due to the special structure of tensors. In this paper, a power-sum function activated RNN model is proposed to find the solutions of the multi-linear systems with nonsingular ${\mathcal{M}}$-tensors. It is theoretically proved that the proposed RNN model is stable in the sense of Lyapunov stability theory and converges to the theoretical solution. In addition, computer simulations are provided to substantiate the effectiveness and superiority of the proposed RNN model.