Noise-tolerant neural algorithm for online solving time-varying full-rank matrix Moore–Penrose inverse problems: A control-theoretic approach

• Published in: Neurocomputing (Amsterdam) Vol. 413; pp. 158 - 172
• Main Authors: Sun, Zhongbo, Li, Feng, Jin, Long, Shi, Tian, Liu, Keping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 06.11.2020
• Subjects: Exponential convergence; Moore–Penrose inverse problems; Recurrent neural network model; Redundant robot manipulators; Time-varying full-rank matrix; Moore–Penrose inverse problems; Exponential convergence; Recurrent neural network model; Redundant robot manipulators; Time-varying full-rank matrix
• ISSN: 0925-2312; 1872-8286
• DOI: 10.1016/j.neucom.2020.06.050

In this paper, zeroing neural network models are redesigned and analyzed from a control-theoretical framework for online solving time-varying full-rank Moore–Penrose inversions. To solve time-varying full-rank Moore–Penrose inverse problems with different noises in real time, some modified zeroing neural network models are developed, analyzed and investigated from the perspective of control. Furthermore, the proposed zeroing neural network models globally converge to the theoretical solution of the full-rank Moore–Penrose inverse problem without noises, and exponentially converge to the exact solution in the presence of noises, which are demonstrated theoretically. Moreover, in comparison with existing models, numerical simulations are provided to substantiate the feasibility and superiority of the proposed modified neural network for online solving time-varying full-rank Moore–Penrose problems with inherent tolerance to noises. In addition, the numerical results infer that different activation functions can be applied to accelerate the convergence speed of the zeroing neural network model. Finally, the proposed zeroing neural network models are applied to the motion generation of redundant robot manipulators, which illustrates its high efficiency and robustness.