Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization
As a special kind of recurrent neural networks, Zhang neural network (ZNN) has been successfully applied to various time-variant problems solving. In this paper, we present three Zhang et al. discretization (ZeaD) formulas, including a special two-step ZeaD formula, a general two-step ZeaD formula,...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/4745759 |
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| author | Min Sun Maoying Tian Yiju Wang |
| author_facet | Min Sun Maoying Tian Yiju Wang |
| author_sort | Min Sun |
| collection | DOAJ |
| description | As a special kind of recurrent neural networks, Zhang neural network (ZNN) has been successfully applied to various time-variant problems solving. In this paper, we present three Zhang et al. discretization (ZeaD) formulas, including a special two-step ZeaD formula, a general two-step ZeaD formula, and a general five-step ZeaD formula, and prove that the special and general two-step ZeaD formulas are convergent while the general five-step ZeaD formula is not zero-stable and thus is divergent. Then, to solve the time-varying nonlinear optimization (TVNO) in real time, based on the Taylor series expansion and the above two convergent two-step ZeaD formulas, we discrete the continuous-time ZNN (CTZNN) model of TVNO and thus get a special two-step discrete-time ZNN (DTZNN) model and a general two-step DTZNN model. Theoretical analyses indicate that the sequence generated by the first DTZNN model is divergent, while the sequence generated by the second DTZNN model is convergent. Furthermore, for the step-size of the second DTZNN model, its tight upper bound and the optimal step-size are also discussed. Finally, some numerical results and comparisons are provided and analyzed to substantiate the efficacy of the proposed DTZNN models. |
| format | Article |
| id | doaj-art-23fdba7061644ad49992edb72211a18f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-23fdba7061644ad49992edb72211a18f2025-02-03T01:23:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/47457594745759Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear OptimizationMin Sun0Maoying Tian1Yiju Wang2School of Mathematics and Statistics, Zaozhuang University, Shandong 277160, ChinaDepartment of Physiology, Shandong Coal Mining Health School, Shandong 277011, ChinaSchool of Management, Qufu Normal University, Shandong 276826, ChinaAs a special kind of recurrent neural networks, Zhang neural network (ZNN) has been successfully applied to various time-variant problems solving. In this paper, we present three Zhang et al. discretization (ZeaD) formulas, including a special two-step ZeaD formula, a general two-step ZeaD formula, and a general five-step ZeaD formula, and prove that the special and general two-step ZeaD formulas are convergent while the general five-step ZeaD formula is not zero-stable and thus is divergent. Then, to solve the time-varying nonlinear optimization (TVNO) in real time, based on the Taylor series expansion and the above two convergent two-step ZeaD formulas, we discrete the continuous-time ZNN (CTZNN) model of TVNO and thus get a special two-step discrete-time ZNN (DTZNN) model and a general two-step DTZNN model. Theoretical analyses indicate that the sequence generated by the first DTZNN model is divergent, while the sequence generated by the second DTZNN model is convergent. Furthermore, for the step-size of the second DTZNN model, its tight upper bound and the optimal step-size are also discussed. Finally, some numerical results and comparisons are provided and analyzed to substantiate the efficacy of the proposed DTZNN models.http://dx.doi.org/10.1155/2019/4745759 |
| spellingShingle | Min Sun Maoying Tian Yiju Wang Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization Discrete Dynamics in Nature and Society |
| title | Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization |
| title_full | Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization |
| title_fullStr | Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization |
| title_full_unstemmed | Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization |
| title_short | Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization |
| title_sort | discrete time zhang neural networks for time varying nonlinear optimization |
| url | http://dx.doi.org/10.1155/2019/4745759 |
| work_keys_str_mv | AT minsun discretetimezhangneuralnetworksfortimevaryingnonlinearoptimization AT maoyingtian discretetimezhangneuralnetworksfortimevaryingnonlinearoptimization AT yijuwang discretetimezhangneuralnetworksfortimevaryingnonlinearoptimization |