Abstract
A special kind of recurrent neural networks (RNN) with implicit dynamics has recently been proposed by Zhang et al, which could be generalized to solve online various time-varying problems. In comparison with conventional gradient neural networks (GNN), such RNN (or termed specifically as Zhang neural networks, ZNN) models are elegantly designed by defining matrix-valued indefinite error functions. In this paper, we generalize and investigate the ZNN and GNN models for online solution of time-varying matrix square roots. In addition, software modeling techniques are investigated to model and simulate both neural-network systems. Computer-modeling results verify that superior convergence and efficacy could be achieved by such ZNN models in this time-varying problem solving, as compared to the GNN models.
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References
Zhang, Y.: Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion. In: Proceedings of IEEE International Symposium on Intelligent Control, Cyprus, pp. 1411–1416 (2005)
Zhang, Y., Ge, S.S.: A General Recurrent Neural Network Model for Time-Varying Matrix Inversion. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Hawaii, pp. 6169–6174 (2003)
Zhang, Y., Jiang, D., Wang, J.: A Recurrent Neural Network for Solving Sylvester Equation with Time-Varying Coefficients. IEEE Transactions on Neural Networks 13(5), 1053–1063 (2002)
Zhang, Y., Peng, H.: Zhang Neural Network for Linear Time-Varying Equation Solving and its Robotic Application. In: Proceedings of the 6th International Conference on Machine Learning and Cybernetics, Hong Kong, pp. 3543–3548 (2007)
Zhang, Y., Guo, X., Ma, W.: Modeling and Simulation of Zhang Neural Network for Online Linear Time-Varying Equations Solving Based on Matlab Simulink. In: Proceedings of the 7th International Conference on Machine Learning and Cybernetics, Kunming, pp. 805–810 (2008)
Ma, W., Zhang, Y., Wang, J.: Matlab Simulink Modeling and Simulation of Zhang Neural Networks for Online Time-Varying Sylvester Equation Solving. In: Proceedings of International Joint Conference on Neural Networks, Hong Kong, pp. 286–290 (2008)
The MathWorks Inc.: Simulink 7 Getting Started Guide, Natick, MA (2008)
Higham, N.J.: Stable Iterations for the Matrix Square Root. Numerical Algorithms 15(2), 227–242 (1997)
Hasan, M.A., Hasan, A.A., Rahman, S.: Fixed Point Iterations for Computing Square Roots and the Matrix Sign Function of Complex Matrices. In: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, pp. 4253–4258 (2000)
Zhang, Y.: On the LVI-Based Primal-Dual Neural Network for Solving Online Linear and Quadratic Programming Problems. In: Proceedings of American Control Conference, Portland, pp. 1351–1356 (2005)
Zhang, Y., Ma, W., Yi, C.: The Link between Newton Iteration for Matrix Inversion and Zhang Neural Network (ZNN). In: Proceedings of IEEE International Conference on Industrial Technology, Singapore, pp. 1–6 (2008)
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© 2009 Springer-Verlag Berlin Heidelberg
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Zhang, Y., Yang, Y., Tan, N. (2009). Time-Varying Matrix Square Roots Solving via Zhang Neural Network and Gradient Neural Network: Modeling, Verification and Comparison. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_2
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DOI: https://doi.org/10.1007/978-3-642-01507-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01506-9
Online ISBN: 978-3-642-01507-6
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