Journal
NEUROCOMPUTING
Volume 133, Issue -, Pages 512-522Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.neucom.2013.12.001
Keywords
Time-varying matrix pseudoinverse; Finite-time convergence; Zhang function; Activation function
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Funding
- National Natural Science Foundation of China [61075121, 60935001]
- Specialized Research Fund for the Doctoral Program of Institutions of Higher Education of China [20100171110045]
- Scientific Research Fund of Hunan Provincial Education Department [13C757]
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In this paper, a special class of recurrent neural network, termed Zhang neural network (ZNN), is investigated for the online solution of the time-varying matrix pseudoinverse. Meanwhile, a novel activation function, named Li activation function, is employed. Then, based on two basic Zhang functions (ZFs) and the intrinsically nonlinear method of ZNN design, two finite-time convergent ZNN models (termed ZNN-1 model and ZNN-2 model) are first proposed and investigated for time-varying matrix pseudoinversion. Such two ZNN models can be accelerated to finite-time convergence to the time-varying theoretical pseudoinverse. The upper bound of the convergence time is also derived analytically via Lyapunov theory. By exploiting the other three simplified ZFs and the extended nonlinearization method, three simplified finite-time convergent ZNN models (termed ZNN-3 model, ZNN-4 model and ZNN-5 model) are sequentially proposed. In addition, the link between the ZNN models and the Getz-Marsden (G-M) dynamic system is discovered and presented in this paper. Computer-simulation results further substantiate the theoretical analysis and demonstrate the effectiveness of ZNN models based on different ZFs for the time-varying matrix pseudoinverse. (C) 2014 Elsevier B.V. All rights reserved.
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