A new super-predefined-time convergence and noise-tolerant RNN for solving time-variant linear matrix–vector inequality in noisy environment and its application to robot arm.

Recurrent neural networks (RNNs) are excellent solvers for time-variant linear matrix–vector inequality (TVLMVI). However, it is difficult for traditional RNNs to track the theoretical solution of TVLMVI under non-ideal conditions [e.g., noisy environment]. Therefore, by introducing a novel nonlinear activation function (NNAF) and time-variant-gain, a new super-predefined-time convergence and noise-tolerant RNN (SPCNT-RNN) is proposed to acquire an online solution to TVLMVI in noisy environment. The difference between SPCNT-RNN and traditional fixed-parameter RNNs (FP-RNNs) is that the error function equation of SPCNT-RNN has NNAF and time-variant-gain coefficient. Due to this difference, the SPCNT-RNN can achieve super-predefined-time convergence in both noise-free and noisy environments, which is superior to that of existing RNNs. The stability, super-predefined-time convergence, and robustness of SPCNT-RNN are theoretically demonstrated. Moreover, the simulation results between various existing RNNs and SPCNT-RNN verify the feasibility, validity, robustness and rapid convergence effect of the proposed SPCNT-RNN. [ABSTRACT FROM AUTHOR]