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.

中文翻译：

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带约束的时变不确定线性系统在线求解的新递归神经网络

最近，递归神经网络（RNN）被视为在线数学问题解决的重要替代方法。通过提出第一个RNN模型来解决带约束的时间相关的不确定线性系统，本文提供了重要的改进。特别地，通过引入时间相关的非负向量，将受约束约束的不确定线性系统首先转换为包含线性和非线性方程的时间相关系统。因此，新构建的RNN模型可以使与时间有关的方程式归零。然后，从理论上证明该模型具有收敛性，并且仿真结果进一步证实了所提出的RNN模型解决带约束的时变不确定线性系统的有效性。最后，