Direct derivation scheme of DT-RNN algorithm for discrete time-variant matrix pseudo-inversion with application to robotic manipulator

The improvement of recurrent neural network (RNN) algorithms is one of target of many researchers, and these algorithms are wieldy used to solve time-variant problems in a variety of domains. A novel direct derivation scheme of discrete time-variant RNN (DT-RNN) algorithm for addressing discrete time-variant matrix pseudo-inversion is discussed in this paper. To be more specific, firstly, a DT-RNN algorithm mathematically founded on the second-order Taylor expansion is proposed for dealing with discrete time-variant matrix pseudo-inversion, and it does not require the theoretical support of continuous time-variant RNN (CT-RNN) algorithm. Secondly, the results of theoretical analyses of the proposed DT-RNN algorithm are also presented in this paper. These results demonstrate that the novel DT-RNN algorithm has remarkable computing performance. The efficiency and applicability of the DT-RNN algorithm have been verified through one numerical experiment example and two robotic manipulator experiments