Noise-Tolerant and Finite-Time Convergent ZNN Models for Dynamic Matrix Moore-Penrose Inversion

• Published in: IEEE transactions on industrial informatics Vol. 16; no. 3; pp. 1591 - 1601
• Main Authors: Tan, Zhiguo, Xiao, Lin, Chen, Siyuan, Lv, Xuanjiao
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.03.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Computer simulation; Convergence; Dynamic Moore–Penrose inverse; evolution formula; finite-time convergence; Informatics; Mathematical model; Neural networks; noise depression; Numerical models; Path tracking; Robot arms; robot inverse kinematic control; Robots; Tracking control; Transmission line matrix methods; Zhang neural network (ZNN) models
• ISSN: 1551-3203; 1941-0050
• DOI: 10.1109/TII.2019.2929055

Dynamic (or say, time-varying) problems have been a hot spot of research recently. As a general form of matrix inverse, dynamic Moore-Penrose inverse solving has received more and more attention owing to its broad applications. The approaches based on neural networks have become a popular solution to various dynamic matrix-related problems including dynamic Moore-Penrose inverse. However, existing neural models either only achieve infinitetime instead of finite-time convergence, or are sensitive to noises. Therefore, finite-time convergent neural model, which is simultaneously capable of addressing the noises, is desperately needed for dynamic Moore-Penrose inverse solving. To do that, in this paper, a novel evolution formula is designed based on the widely investigated Zhang neural network (ZNN). Accordingly, two modified ZNN models (MZNN), namely MZNN-R and MZNN-L models, are proposed and analyzed for the right and left dynamic Moore-Penrose inversion of full-rank matrices, respectively. In addition to providing detailed theoretical analyses on the desired finite-time convergence and noise-depression properties of the proposed two models, we also perform two numerical examples for further verification. Furthermore, to illustrate the potential of MZNN models in practical applications, two path-tracking control examples are also presented via a two-dimensional planar three-link and a three-dimensional Kinova Jaco 2 redundant robot manipulator. The feasibility, extraordinary efficacy, and superiority of the proposed MZNN models for dynamic Moore-Penrose inverse solving are corroborated by both theoretical results and simulation observations.