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

• Published in: Applied soft computing Vol. 133; p. 109861
• Main Authors: Shi, Yang, Zhao, Wenhan, Li, Shuai, Li, Bin, Sun, Xiaobing
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2023
• Subjects: Direct derivation scheme; Discrete time-variant matrix pseudo-inversion; Discrete time-variant recurrent neural network (DT-RNN); Robotic manipulator; Second-order Taylor expansion; Discrete time-variant recurrent neural network (DT-RNN); Second-order Taylor expansion; Direct derivation scheme; Robotic manipulator; Discrete time-variant matrix pseudo-inversion
• ISSN: 1568-4946; 1872-9681; 1872-9681
• DOI: 10.1016/j.asoc.2022.109861

The improvement of recurrent neural network (RNN) algorithms is one of targets of many researchers, and these algorithms are widely 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 and two robotic manipulator experiments. A direct derivation scheme founded on the second-order Taylor expansion has been proposed to establish discrete time-variant recurrent neural network algorithm for discrete time-variant matrix pseudo-inversion, and the solving process has no longer required the theoretical support of continuous time-variant background. The feasibility of algorithm has been proved in this paper, and two application experiments of robotic manipulator have been shown to further validate the efficiency and practicability of such recurrent neural network algorithm.