Abstract
Different from gradient-based neural networks, a special kind of recurrent neural network has recently been proposed by Zhang et al for real-time solution of time-varying problems. In this paper, we generalize such a design method to solving online the time-varying Sylvester equation. In comparison with gradient-based neural networks, the resultant Zhang neural network for solving time-varying Sylvester equation is designed based on a matrix-valued error function, instead of a scalar-valued error function. It is depicted in an implicit dynamics, instead of an explicit dynamics. Furthermore, Zhang neural network globally exponentially converges to the exact solution of the time-varying Sylvester equation. Simulation results substantiate the theoretical analysis and demonstrate the efficacy of Zhang neural network on time-varying problem solving, especially when using a power-sigmoid activation function.
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Zhang, Y., Fan, Z., Li, Z. (2007). Zhang Neural Network for Online Solution of Time-Varying Sylvester Equation. In: Kang, L., Liu, Y., Zeng, S. (eds) Advances in Computation and Intelligence. ISICA 2007. Lecture Notes in Computer Science, vol 4683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74581-5_30
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DOI: https://doi.org/10.1007/978-3-540-74581-5_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74580-8
Online ISBN: 978-3-540-74581-5
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