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

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 t...

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Bibliographic Details
Published in:IEEE transactions on industrial informatics 2020-03, Vol.16 (3), p.1591-1601
Main Authors: Tan, Zhiguo, Xiao, Lin, Chen, Siyuan, Lv, Xuanjiao
Format: Article
Language:English
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
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Summary: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.
ISSN:1551-3203
1941-0050
DOI:10.1109/TII.2019.2929055