| Citation: |
Ting-Jia Liu, Mengyao Li, Ruijuan Zhao, Shu-Xin Miao. A NOISE-TOLERANT AND FIXED-TIME ZEROING NEURAL NETWORK MODEL FOR SOLVING MULTI-LINEAR $ \mathcal{M} $-TENSOR EQUATIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 524-539. doi: 10.11948/20250257
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A NOISE-TOLERANT AND FIXED-TIME ZEROING NEURAL NETWORK MODEL FOR SOLVING MULTI-LINEAR $ \mathcal{M} $-TENSOR EQUATIONS
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Abstract
Zeroing neural network (ZNN) models are effective methods for solving multi-linear systems. To improve the performance of ZNN models, a new ZNN model is proposed for solving multi-linear systems with $ \mathcal{M} $-tensor in this paper. The proposed ZNN model incorporates with a nonlinear activation function. Convergence and robustness of the proposed ZNN model are analyzed. Theoretical results reveal that the proposed ZNN model converges within a fixed time and tolerates different types of noise. Numerical experiments illustrate that the proposed ZNN model is more powerful than some existing ZNN models for solving multi-linear systems with $ \mathcal{M} $-tensor.
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Keywords:
- Multi-linear system /
- ZNN model /
- fixed-time convergence /
- noise-tolerant
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References
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Ting-Jia Liu, Mengyao Li, Ruijuan Zhao, Shu-Xin Miao. A NOISE-TOLERANT AND FIXED-TIME ZEROING NEURAL NETWORK MODEL FOR SOLVING MULTI-LINEAR $ \mathcal{M} $-TENSOR EQUATIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 524-539. doi: 10.11948/20250257
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Figure 1.
The comparison of the FTCNTZNN and CTNN, FTZNN for solving Example 5.1.
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Figure 2.
The comparison of the FTCNTZNN and CTNN, FTZNN with different noise for solving Example 5.1.
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Figure 3.
m=3, n=5 FTCNTZNN model with different parameters under Case 2.
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Figure 4.
The convergence rate of different models for solving Example 5.2.
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Figure 5.
The dynamic bounded vanishing noise of different models for solving Example 5.2.
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Figure 6.
The dynamic bounded non-vanishing noise of different models for solving Example 5.2.