Prescribed-Time Convergent Adaptive ZNN for Time-Varying Matrix Inversion under Harmonic Noise

Harmonic noises widely exist in industrial fields and always affect the computational accuracy of neural network models. The existing original adaptive zeroing neural network (OAZNN) model can effectively suppress harmonic noises. Nevertheless, the OAZNN model’s convergence rate only stays at the exponential convergence, that is, its convergence speed is usually greatly affected by the initial state. Consequently, to tackle the above issue, this work combines the dynamic characteristics of harmonic signals with prescribed-time convergence activation function, and proposes a prescribed-time convergent adaptive ZNN (PTCAZNN) for solving time-varying matrix inverse problem (TVMIP) under harmonic noises. Owing to the nonlinear activation function used having the ability to reject noises itself and the adaptive term also being able to compensate the influence of noises, the PTCAZNN model can realize double noise suppression. More importantly, the theoretical analysis of PTCAZNN model with prescribed-time convergence and robustness performance is provided. Finally, by varying a series of conditions such as the frequency of single harmonic noise, the frequency of multi-harmonic noise, and the initial value and the dimension of the matrix, the comparative simulation results further confirm the effectiveness and superiority of the PTCAZNN model.

Robustness Analyses and Optimal Sampling Gap of Recurrent Neural Network for Dynamic Matrix Pseudoinversion

This study analyses the robustness and convergence characteristics of a neural network. First, a special class of recurrent neural network (RNN), termed a continuous-time Zhang neural network (CTZNN) model, is presented and investigated for dynamic matrix pseudoinversion. Theoretical analysis of the CTZNN model demonstrates that it has good robustness against various types of noise. In addition, considering the requirements of digital implementation and online computation, the optimal sampling gap for a discrete-time Zhang neural network (DTZNN) model under noisy environments is proposed. Finally, experimental results are presented, which further substantiate the theoretical analyses and demonstrate the effectiveness of the proposed ZNN models for computing a dynamic matrix pseudoinverse under noisy environments.