An Arbitrarily Predefined-Time Convergent RNN for Dynamic LMVE With Its Applications in UR3 Robotic Arm Control and Multiagent Systems

Zeroing neural network (ZNN), as a special type of recurrent neural network (RNN), is very competitive in solving time-varying linear matrix-vector equations. Recently, various ZNNs with predefined-time convergence (PTC) capabilities have been reported. Such ZNNs with PTC capabilities can achieve the predefined convergence time via explicitly presetting multiple parameters related to the upper bounds of their convergence time. However, obtaining suitable and robust values for these parameters through reasonable adjustments is a challenging task in many engineering applications. To address this problem, we propose a novel arbitrarily predefined-time convergent RNN (APTC-RNN) with a novel nonlinear piecewise activation-function (NPAF). Unlike most existing ZNNs with PTC capabilities, the proposed APTC-RNN, due to its NPAF, can achieve arbitrarily PTC (APTC) without adjusting any upper bound parameters. Furthermore, due to the piecewise computation form of the NPAF, the proposed APTC-RNN can provide a lower computational cost compared to most existing RNNs. The stability and APTC capability of the proposed APTC-RNN are proven by rigorous theoretical analysis and mathematical derivation. Numerical simulations show that APTC-RNN has faster and more accurate PTC capability than three state-of-the-art RNNs, while having less computational time. Finally, the practicality of the APTC-RNN is verified by applying it to the UR3 robotic arm and multiagent systems.