Gradient-based neural networks for solving periodic Sylvester matrix equations
This paper considers neural network solutions of a category of matrix equation called periodic Sylvester matrix equation (PSME), which appear in the process of periodic system analysis and design. A linear gradient-based neural network (GNN) model aimed at solving the PSME is constructed, whose stat...
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| Published in | Journal of the Franklin Institute Vol. 359; no. 18; pp. 10849 - 10866 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.12.2022
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| Abstract | This paper considers neural network solutions of a category of matrix equation called periodic Sylvester matrix equation (PSME), which appear in the process of periodic system analysis and design. A linear gradient-based neural network (GNN) model aimed at solving the PSME is constructed, whose state is able to converge to the unknown matrix of the equation. In order to obtain a better convergence effect, the linear GNN model is extended to a nonlinear form through the intervention of appropriate activation functions, and its convergence is proved through theoretical derivation. Furthermore, the different convergence effects presented by the model with various activation functions are also explored and analyzed, for instance, the global exponential convergence and the global finite time convergence can be realized. Finally, the numerical examples are used to confirm the validity of the proposed GNN model for solving the PSME considered in this paper as well as the superiority in terms of the convergence effect presented by the model with different activation functions. |
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| AbstractList | This paper considers neural network solutions of a category of matrix equation called periodic Sylvester matrix equation (PSME), which appear in the process of periodic system analysis and design. A linear gradient-based neural network (GNN) model aimed at solving the PSME is constructed, whose state is able to converge to the unknown matrix of the equation. In order to obtain a better convergence effect, the linear GNN model is extended to a nonlinear form through the intervention of appropriate activation functions, and its convergence is proved through theoretical derivation. Furthermore, the different convergence effects presented by the model with various activation functions are also explored and analyzed, for instance, the global exponential convergence and the global finite time convergence can be realized. Finally, the numerical examples are used to confirm the validity of the proposed GNN model for solving the PSME considered in this paper as well as the superiority in terms of the convergence effect presented by the model with different activation functions. |
| Author | Chen, Jinbo Lv, Lingling Zhang, Lei Zhang, Fengrui |
| Author_xml | – sequence: 1 givenname: Lingling surname: Lv fullname: Lv, Lingling email: lingling_lv@163.com organization: Institute of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou 450011, China – sequence: 2 givenname: Jinbo surname: Chen fullname: Chen, Jinbo email: 358490693@qq.com organization: Institute of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou 450011, China – sequence: 3 givenname: Lei orcidid: 0000-0002-8092-3459 surname: Zhang fullname: Zhang, Lei email: zhanglei@henu.edu.cn organization: Henan Key Laboratory of Big Data Analysis and Processing, Henan University; Institute of Data and Knowledge Engineering, School of Computer and Information Engineering, Henan University, Kaifeng 475004, China – sequence: 4 givenname: Fengrui orcidid: 0000-0001-7656-1267 surname: Zhang fullname: Zhang, Fengrui email: zhangfengrui@ncwu.edu.cn organization: Institute of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou 450011, China |
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| Cites_doi | 10.1016/j.sysconle.2008.12.004 10.1109/TAC.2005.852558 10.1016/j.jfranklin.2018.07.015 10.1016/j.jfranklin.2014.09.011 10.1109/TAC.2006.874989 10.1016/j.jfranklin.2018.07.045 10.1016/j.neucom.2016.02.021 10.1109/TAC.2014.2326273 10.1016/j.jfranklin.2017.01.004 10.1016/j.automatica.2018.07.021 10.3724/SP.J.1004.2010.00113 10.1002/mma.7030 10.1049/el:19920311 10.1109/TII.2017.2717020 10.1007/s11063-012-9241-1 10.1109/TNN.2002.1031938 10.1016/j.ipl.2013.09.002 10.3934/jimo.2017053 10.1016/j.ipl.2018.10.004 10.1049/cje.2017.06.007 10.1007/s12190-018-01220-3 10.1109/TCYB.2020.2996743 10.1109/TII.2021.3130237 10.1016/j.jfranklin.2017.09.029 10.2298/FIL1609503H 10.3724/SP.J.1004.2009.01136 10.1002/rnc.3076 10.1016/j.jfranklin.2019.12.031 10.1109/TAC.2009.2023779 10.1016/j.neucom.2020.08.061 10.1002/asjc.1528 10.1007/s00034-012-9421-2 10.1016/j.automatica.2010.10.011 10.1016/j.automatica.2017.06.012 10.1049/iet-cta.2013.1044 10.1016/j.jfranklin.2020.11.022 10.1016/j.automatica.2011.04.015 10.1002/acs.3029 |
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| References | Lv, Duan, Zhou (bib0002) 2010; 36 Xiao, Li, Tan, Zhang, Liao, Chen, Jin, Li (bib0034) 2019; 142 Chen, Yi, Qiao (bib0030) 2013; 113 Duan, Zhou (bib0015) 2006; 51 Zhang, Chen, Tan (bib0024) 2009; 54 Ding, Liu, Ding (bib0028) 2008; 197 Sun, Wu, Liu (bib0031) 2021; 453 Ding, Zhang (bib0019) 2014; 8 Zhou, Li, Lin (bib0003) 2015; 25 Lv, Zhang, Zhang, Wang (bib0035) 2018; 14 Lv, Zhang, Zhang, Liu (bib0022) 2018; 355 Xiao, Liao, Li, Zhang, Ding, Jin (bib0023) 2018; 14 Liu, Feng, Yang (bib0029) 2012; 31 L. Lv, Z. Wu, J. Zhang, Z. Tan, L. Zhang and Z. Tian, “A VMD and LSTM based hybrid model of load forecasting for power grid security,” in IEEE Transactions on Industrial Informatics, doi Li, Liu, Ding (bib0027) 2019; 33 Zhou, Duan, Lin (bib0005) 2011; 47 Ren, He, Luan, Liu, Karimi (bib0007) 2021; 51 Lv, Zhang, Zhang (bib0010) 2017; 354 Shuai, Chen, Bo (bib0032) 2013; 37 Lv, Tang, Zhang (bib0008) 2020; 357 Ding, Chen (bib0017) 2005; 50 Wu, Zhang, Zhang (bib0011) 2018; 87 Zhou (bib0013) 2018; 355 Zhang, Chen, Chen (bib0039) 2009; 35 Zhou, Wei, Duan (bib0001) 2011; 47 Hajarian, Chronopoulos (bib0014) 2021; 44 Lv, Zhang (bib0009) 2016; 353 Zhou, Duan, Li (bib0018) 2009; 58 J (bib0038) 1992; 28 Hajarian (bib0016) 2016; 30 Xiao, Lu (bib0025) 2017; 26 Hajarian (bib0037) 2018; 20 Zhang, Jiang, Wang (bib0026) 2002; 13 . Sun, Wang (bib0036) 2019; 60 Duan, Lv, Zhou (bib0004) 2009 Lv, Zhang (bib0021) 2017; 354 Lv, Chen, Zhang, Wang, Zhang (bib0040) 2020; 358 Xiao, Liao (bib0033) 2016; 193 Wu, Sun, Zhang (bib0020) 2018; 97 Wu, Duan (bib0012) 2015; 60 Ren, He (bib0006) 2020; 365 Li (10.1016/j.jfranklin.2022.05.023_bib0027) 2019; 33 Hajarian (10.1016/j.jfranklin.2022.05.023_bib0014) 2021; 44 Duan (10.1016/j.jfranklin.2022.05.023_bib0004) 2009 Zhou (10.1016/j.jfranklin.2022.05.023_bib0005) 2011; 47 Zhou (10.1016/j.jfranklin.2022.05.023_bib0013) 2018; 355 10.1016/j.jfranklin.2022.05.023_bib0041 Xiao (10.1016/j.jfranklin.2022.05.023_bib0034) 2019; 142 Ren (10.1016/j.jfranklin.2022.05.023_bib0006) 2020; 365 Zhang (10.1016/j.jfranklin.2022.05.023_bib0024) 2009; 54 Zhou (10.1016/j.jfranklin.2022.05.023_bib0001) 2011; 47 Duan (10.1016/j.jfranklin.2022.05.023_bib0015) 2006; 51 Ding (10.1016/j.jfranklin.2022.05.023_bib0017) 2005; 50 Lv (10.1016/j.jfranklin.2022.05.023_bib0008) 2020; 357 Lv (10.1016/j.jfranklin.2022.05.023_bib0021) 2017; 354 Chen (10.1016/j.jfranklin.2022.05.023_bib0030) 2013; 113 Zhou (10.1016/j.jfranklin.2022.05.023_bib0003) 2015; 25 Ding (10.1016/j.jfranklin.2022.05.023_bib0028) 2008; 197 Xiao (10.1016/j.jfranklin.2022.05.023_bib0033) 2016; 193 Ding (10.1016/j.jfranklin.2022.05.023_bib0019) 2014; 8 Xiao (10.1016/j.jfranklin.2022.05.023_bib0025) 2017; 26 Wu (10.1016/j.jfranklin.2022.05.023_bib0012) 2015; 60 J (10.1016/j.jfranklin.2022.05.023_bib0038) 1992; 28 Liu (10.1016/j.jfranklin.2022.05.023_bib0029) 2012; 31 Lv (10.1016/j.jfranklin.2022.05.023_bib0035) 2018; 14 Wu (10.1016/j.jfranklin.2022.05.023_bib0020) 2018; 97 Shuai (10.1016/j.jfranklin.2022.05.023_bib0032) 2013; 37 Wu (10.1016/j.jfranklin.2022.05.023_bib0011) 2018; 87 Zhang (10.1016/j.jfranklin.2022.05.023_bib0026) 2002; 13 Lv (10.1016/j.jfranklin.2022.05.023_bib0002) 2010; 36 Zhou (10.1016/j.jfranklin.2022.05.023_bib0018) 2009; 58 Lv (10.1016/j.jfranklin.2022.05.023_bib0040) 2020; 358 Sun (10.1016/j.jfranklin.2022.05.023_bib0036) 2019; 60 Xiao (10.1016/j.jfranklin.2022.05.023_bib0023) 2018; 14 Lv (10.1016/j.jfranklin.2022.05.023_bib0009) 2016; 353 Sun (10.1016/j.jfranklin.2022.05.023_bib0031) 2021; 453 Lv (10.1016/j.jfranklin.2022.05.023_bib0010) 2017; 354 Hajarian (10.1016/j.jfranklin.2022.05.023_bib0037) 2018; 20 Hajarian (10.1016/j.jfranklin.2022.05.023_bib0016) 2016; 30 Lv (10.1016/j.jfranklin.2022.05.023_bib0022) 2018; 355 Zhang (10.1016/j.jfranklin.2022.05.023_bib0039) 2009; 35 Ren (10.1016/j.jfranklin.2022.05.023_bib0007) 2021; 51 |
| References_xml | – volume: 353 start-page: 1005 year: 2016 end-page: 1018 ident: bib0009 article-title: On the periodic Sylvester equations and their applications in periodic Luenberger observers design publication-title: J. Franklin Inst. – volume: 51 start-page: 805 year: 2006 end-page: 809 ident: bib0015 article-title: Solution to the second-order Sylvester matrix equation MVF2+DVF+KV=BW publication-title: IEEE Trans. Automat. Control – volume: 60 start-page: 289 year: 2015 end-page: 294 ident: bib0012 article-title: New iterative algorithms for solving coupled Markovian jump Lyapunov equations publication-title: IEEE Trans. Automat. Control – year: 2009 ident: bib0004 article-title: Robust pole assignment for discrete-time linear periodic systems via output feedback publication-title: Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, combined withe the 28th Chinese Control Conference, December 16–18, 2009, Shanghai, China – volume: 33 start-page: 1189 year: 2019 end-page: 1211 ident: bib0027 article-title: The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle publication-title: Int. J. Adapt Control Signal Process. – volume: 355 start-page: 7246 year: 2018 end-page: 7280 ident: bib0013 article-title: Solutions to linear bimatrix equations with applications to pole assignment of complex-valued linear systems publication-title: J. Franklin Inst. – reference: L. Lv, Z. Wu, J. Zhang, Z. Tan, L. Zhang and Z. Tian, “A VMD and LSTM based hybrid model of load forecasting for power grid security,” in IEEE Transactions on Industrial Informatics, doi: – volume: 35 start-page: 1136 year: 2009 end-page: 1139 ident: bib0039 article-title: Convergence properties analysis of gradient neural network for solving online linear equations publication-title: Acta Autom. Sin. – volume: 87 start-page: 395 year: 2018 end-page: 403 ident: bib0011 article-title: An iterative algorithm for discrete periodic Lyapunov matrix equations publication-title: Automatica – volume: 20 start-page: 1 year: 2018 end-page: 9 ident: bib0037 article-title: Matrix form of biconjugate residual algorithm to solve the discrete-time periodic Sylvester matrix equations publication-title: Asian J. Control – volume: 365 start-page: 124631 year: 2020 ident: bib0006 article-title: Finite-time stabilization for positive Markovian jumping neural networks publication-title: Appl. Math. Comput. – volume: 14 start-page: 413 year: 2018 end-page: 425 ident: bib0035 article-title: An iterative algorithm for periodic Sylvester matrix equations publication-title: J. Ind. Manage. Optim. – volume: 354 start-page: 2358 year: 2017 end-page: 2370 ident: bib0021 article-title: Finite iterative solutions to periodic Sylvester matrix equations publication-title: J. Franklin Inst. – volume: 355 start-page: 7691 year: 2018 end-page: 7705 ident: bib0022 article-title: Gradient based approach for generalized discrete-time periodic coupled Sylvester matrix equations publication-title: J. Franklin Inst. – volume: 113 start-page: 876 year: 2013 end-page: 881 ident: bib0030 article-title: Improved neural solution for the Lyapunov matrix equation based on gradient search publication-title: Inf. Process. Lett. – volume: 357 start-page: 3601 year: 2020 end-page: 3621 ident: bib0008 article-title: Parametric solutions to generalized periodic Sylvester bimatrix equations publication-title: J. Franklin Inst. – volume: 97 start-page: 38 year: 2018 end-page: 47 ident: bib0020 article-title: An SOR implicit iterative algorithm for coupled Lyapunov equations publication-title: Automatica – volume: 14 start-page: 98 year: 2018 end-page: 105 ident: bib0023 article-title: Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator publication-title: IEEE Trans. Ind. Inf. – volume: 30 start-page: 2503 year: 2016 end-page: 2520 ident: bib0016 article-title: Extending the CGLS method for finding the least squares solutions of general discrete-time periodic matrix equations publication-title: Filomat – volume: 354 start-page: 8057 year: 2017 end-page: 8071 ident: bib0010 article-title: A parametric poles assignment algorithm for second-order linear periodic systems publication-title: J. Franklin Inst. – volume: 26 start-page: 1194 year: 2017 end-page: 1197 ident: bib0025 article-title: A fully complex-valued gradient neural network for rapidly computing complex-valued linear matrix equations publication-title: Chin. J. Electron. – volume: 13 start-page: 1053 year: 2002 end-page: 1063 ident: bib0026 article-title: A recurrent neural network for solving Sylvester equation with time-varying coefficients publication-title: IEEE Trans. Neural Netw. – volume: 58 start-page: 327 year: 2009 end-page: 333 ident: bib0018 article-title: Gradient based iterative algorithm for solving coupled matrix equations publication-title: Syst. Control Lett. – volume: 37 start-page: 189 year: 2013 end-page: 205 ident: bib0032 article-title: Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function publication-title: Neural Process. Lett. – volume: 60 start-page: 413 year: 2019 end-page: 434 ident: bib0036 article-title: The conjugate gradient methods for solving the generalized periodic Sylvester matrix equations publication-title: J. Appl. Math. Comput. – volume: 44 start-page: 4297 year: 2021 end-page: 4315 ident: bib0014 article-title: Least-squares partially bisymmetric solutions of coupled Sylvester matrix equations accompanied by a prescribed submatrix constraint publication-title: Math. Methods Appl. Sci. – volume: 31 start-page: 1985 year: 2012 end-page: 2000 ident: bib0029 article-title: Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle publication-title: Circuits Syst. Signal Process. – volume: 54 start-page: 1940 year: 2009 end-page: 1945 ident: bib0024 article-title: Performance analysis of gradient neural network exploited for online time-varying matrix inversion publication-title: IEEE Trans. Automat. Control – volume: 358 start-page: 2039 year: 2020 end-page: 2059 ident: bib0040 article-title: A numerical solution of a class of periodic coupled matrix equations publication-title: J. Franklin Inst. – volume: 453 start-page: 599 year: 2021 end-page: 609 ident: bib0031 article-title: Gradient-based neural networks for online solutions of coupled Lyapunov matrix equations publication-title: Neurocomputing – volume: 142 start-page: 35 year: 2019 end-page: 40 ident: bib0034 article-title: Nonlinear gradient neural network for solving system of linear equations publication-title: Inf. Process. Lett – volume: 36 start-page: 113 year: 2010 end-page: 120 ident: bib0002 article-title: Parametric pole assignment for discrete-time linear periodic systems via output feedback publication-title: Acta Autom. Sin. – volume: 47 start-page: 316 year: 2011 end-page: 325 ident: bib0005 article-title: A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation publication-title: Automatica – reference: . – volume: 25 start-page: 103 year: 2015 end-page: 124 ident: bib0003 article-title: Control of discrete-time periodic linear systems with input saturation via multi-step periodic invariant sets publication-title: Int. J. Robust Nonlinear Control – volume: 28 start-page: 493 year: 1992 end-page: 495 ident: bib0038 article-title: Electronic realization of recurrent neural network for solving simultaneous linear equation publication-title: Electron. Lett – volume: 50 start-page: 1216 year: 2005 end-page: 1221 ident: bib0017 article-title: Gradient based iterative algorithms for solving a class of matrix equations publication-title: IEEE Trans. Automat. Control – volume: 193 start-page: 213 year: 2016 end-page: 218 ident: bib0033 article-title: A convergence-accelerated Zhang neural network and its solution application to Lyapunov equation publication-title: Neurocomputing – volume: 8 start-page: 1588 year: 2014 end-page: 1595 ident: bib0019 article-title: Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems publication-title: IET Control Theory Appl. – volume: 47 start-page: 1813 year: 2011 end-page: 1820 ident: bib0001 article-title: Stability and stabilization of discrete-time periodic linear systems with actuator saturation publication-title: Automatica – volume: 51 start-page: 77 year: 2021 end-page: 87 ident: bib0007 article-title: Finite-time L2-gain asynchronous control for continuous-time positive hidden Markov jump systems via T’S fuzzy model approach publication-title: IEEE Trans. Cybern. – volume: 197 start-page: 41 year: 2008 end-page: 50 ident: bib0028 article-title: Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle publication-title: Appl. Math. Comput. – volume: 58 start-page: 327 issue: 5 year: 2009 ident: 10.1016/j.jfranklin.2022.05.023_bib0018 article-title: Gradient based iterative algorithm for solving coupled matrix equations publication-title: Syst. Control Lett. doi: 10.1016/j.sysconle.2008.12.004 – volume: 365 start-page: 124631 year: 2020 ident: 10.1016/j.jfranklin.2022.05.023_bib0006 article-title: Finite-time stabilization for positive Markovian jumping neural networks publication-title: Appl. Math. Comput. – volume: 197 start-page: 41 issue: 1 year: 2008 ident: 10.1016/j.jfranklin.2022.05.023_bib0028 article-title: Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle publication-title: Appl. Math. Comput. – volume: 50 start-page: 1216 issue: 8 year: 2005 ident: 10.1016/j.jfranklin.2022.05.023_bib0017 article-title: Gradient based iterative algorithms for solving a class of matrix equations publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2005.852558 – volume: 355 start-page: 7246 issue: 15 year: 2018 ident: 10.1016/j.jfranklin.2022.05.023_bib0013 article-title: Solutions to linear bimatrix equations with applications to pole assignment of complex-valued linear systems publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2018.07.015 – volume: 353 start-page: 1005 issue: 5 year: 2016 ident: 10.1016/j.jfranklin.2022.05.023_bib0009 article-title: On the periodic Sylvester equations and their applications in periodic Luenberger observers design publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2014.09.011 – volume: 51 start-page: 805 issue: 5 year: 2006 ident: 10.1016/j.jfranklin.2022.05.023_bib0015 article-title: Solution to the second-order Sylvester matrix equation MVF2+DVF+KV=BW publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2006.874989 – volume: 355 start-page: 7691 issue: 15 year: 2018 ident: 10.1016/j.jfranklin.2022.05.023_bib0022 article-title: Gradient based approach for generalized discrete-time periodic coupled Sylvester matrix equations publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2018.07.045 – volume: 193 start-page: 213 issue: Jun.12 year: 2016 ident: 10.1016/j.jfranklin.2022.05.023_bib0033 article-title: A convergence-accelerated Zhang neural network and its solution application to Lyapunov equation publication-title: Neurocomputing doi: 10.1016/j.neucom.2016.02.021 – volume: 60 start-page: 289 issue: 1 year: 2015 ident: 10.1016/j.jfranklin.2022.05.023_bib0012 article-title: New iterative algorithms for solving coupled Markovian jump Lyapunov equations publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2014.2326273 – year: 2009 ident: 10.1016/j.jfranklin.2022.05.023_bib0004 article-title: Robust pole assignment for discrete-time linear periodic systems via output feedback – volume: 354 start-page: 2358 issue: 5 year: 2017 ident: 10.1016/j.jfranklin.2022.05.023_bib0021 article-title: Finite iterative solutions to periodic Sylvester matrix equations publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2017.01.004 – volume: 97 start-page: 38 year: 2018 ident: 10.1016/j.jfranklin.2022.05.023_bib0020 article-title: An SOR implicit iterative algorithm for coupled Lyapunov equations publication-title: Automatica doi: 10.1016/j.automatica.2018.07.021 – volume: 36 start-page: 113 issue: 1 year: 2010 ident: 10.1016/j.jfranklin.2022.05.023_bib0002 article-title: Parametric pole assignment for discrete-time linear periodic systems via output feedback publication-title: Acta Autom. Sin. doi: 10.3724/SP.J.1004.2010.00113 – volume: 44 start-page: 4297 issue: 6 year: 2021 ident: 10.1016/j.jfranklin.2022.05.023_bib0014 article-title: Least-squares partially bisymmetric solutions of coupled Sylvester matrix equations accompanied by a prescribed submatrix constraint publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.7030 – volume: 28 start-page: 493 issue: 5 year: 1992 ident: 10.1016/j.jfranklin.2022.05.023_bib0038 article-title: Electronic realization of recurrent neural network for solving simultaneous linear equation publication-title: Electron. Lett doi: 10.1049/el:19920311 – volume: 14 start-page: 98 issue: 5 year: 2018 ident: 10.1016/j.jfranklin.2022.05.023_bib0023 article-title: Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator publication-title: IEEE Trans. Ind. Inf. doi: 10.1109/TII.2017.2717020 – volume: 37 start-page: 189 issue: 2 year: 2013 ident: 10.1016/j.jfranklin.2022.05.023_bib0032 article-title: Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function publication-title: Neural Process. Lett. doi: 10.1007/s11063-012-9241-1 – volume: 13 start-page: 1053 issue: 5 year: 2002 ident: 10.1016/j.jfranklin.2022.05.023_bib0026 article-title: A recurrent neural network for solving Sylvester equation with time-varying coefficients publication-title: IEEE Trans. Neural Netw. doi: 10.1109/TNN.2002.1031938 – volume: 113 start-page: 876 issue: 22–24 year: 2013 ident: 10.1016/j.jfranklin.2022.05.023_bib0030 article-title: Improved neural solution for the Lyapunov matrix equation based on gradient search publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2013.09.002 – volume: 14 start-page: 413 issue: 1 year: 2018 ident: 10.1016/j.jfranklin.2022.05.023_bib0035 article-title: An iterative algorithm for periodic Sylvester matrix equations publication-title: J. Ind. Manage. Optim. doi: 10.3934/jimo.2017053 – volume: 142 start-page: 35 issue: FEB year: 2019 ident: 10.1016/j.jfranklin.2022.05.023_bib0034 article-title: Nonlinear gradient neural network for solving system of linear equations publication-title: Inf. Process. Lett doi: 10.1016/j.ipl.2018.10.004 – volume: 26 start-page: 1194 issue: 6 year: 2017 ident: 10.1016/j.jfranklin.2022.05.023_bib0025 article-title: A fully complex-valued gradient neural network for rapidly computing complex-valued linear matrix equations publication-title: Chin. J. Electron. doi: 10.1049/cje.2017.06.007 – volume: 60 start-page: 413 issue: 1–2 year: 2019 ident: 10.1016/j.jfranklin.2022.05.023_bib0036 article-title: The conjugate gradient methods for solving the generalized periodic Sylvester matrix equations publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-018-01220-3 – volume: 51 start-page: 77 issue: 1 year: 2021 ident: 10.1016/j.jfranklin.2022.05.023_bib0007 article-title: Finite-time L2-gain asynchronous control for continuous-time positive hidden Markov jump systems via T’S fuzzy model approach publication-title: IEEE Trans. Cybern. doi: 10.1109/TCYB.2020.2996743 – ident: 10.1016/j.jfranklin.2022.05.023_bib0041 doi: 10.1109/TII.2021.3130237 – volume: 354 start-page: 8057 issue: 18 year: 2017 ident: 10.1016/j.jfranklin.2022.05.023_bib0010 article-title: A parametric poles assignment algorithm for second-order linear periodic systems publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2017.09.029 – volume: 30 start-page: 2503 issue: 9 year: 2016 ident: 10.1016/j.jfranklin.2022.05.023_bib0016 article-title: Extending the CGLS method for finding the least squares solutions of general discrete-time periodic matrix equations publication-title: Filomat doi: 10.2298/FIL1609503H – volume: 35 start-page: 1136 issue: 8 year: 2009 ident: 10.1016/j.jfranklin.2022.05.023_bib0039 article-title: Convergence properties analysis of gradient neural network for solving online linear equations publication-title: Acta Autom. Sin. doi: 10.3724/SP.J.1004.2009.01136 – volume: 25 start-page: 103 issue: 1 year: 2015 ident: 10.1016/j.jfranklin.2022.05.023_bib0003 article-title: Control of discrete-time periodic linear systems with input saturation via multi-step periodic invariant sets publication-title: Int. J. Robust Nonlinear Control doi: 10.1002/rnc.3076 – volume: 357 start-page: 3601 issue: 6 year: 2020 ident: 10.1016/j.jfranklin.2022.05.023_bib0008 article-title: Parametric solutions to generalized periodic Sylvester bimatrix equations publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2019.12.031 – volume: 54 start-page: 1940 issue: 8 year: 2009 ident: 10.1016/j.jfranklin.2022.05.023_bib0024 article-title: Performance analysis of gradient neural network exploited for online time-varying matrix inversion publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2009.2023779 – volume: 453 start-page: 599 year: 2021 ident: 10.1016/j.jfranklin.2022.05.023_bib0031 article-title: Gradient-based neural networks for online solutions of coupled Lyapunov matrix equations publication-title: Neurocomputing doi: 10.1016/j.neucom.2020.08.061 – volume: 20 start-page: 1 issue: 1 year: 2018 ident: 10.1016/j.jfranklin.2022.05.023_bib0037 article-title: Matrix form of biconjugate residual algorithm to solve the discrete-time periodic Sylvester matrix equations publication-title: Asian J. Control doi: 10.1002/asjc.1528 – volume: 31 start-page: 1985 issue: 6 year: 2012 ident: 10.1016/j.jfranklin.2022.05.023_bib0029 article-title: Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle publication-title: Circuits Syst. Signal Process. doi: 10.1007/s00034-012-9421-2 – volume: 47 start-page: 316 issue: 2 year: 2011 ident: 10.1016/j.jfranklin.2022.05.023_bib0005 article-title: A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation publication-title: Automatica doi: 10.1016/j.automatica.2010.10.011 – volume: 87 start-page: 395 year: 2018 ident: 10.1016/j.jfranklin.2022.05.023_bib0011 article-title: An iterative algorithm for discrete periodic Lyapunov matrix equations publication-title: Automatica doi: 10.1016/j.automatica.2017.06.012 – volume: 8 start-page: 1588 year: 2014 ident: 10.1016/j.jfranklin.2022.05.023_bib0019 article-title: Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2013.1044 – volume: 358 start-page: 2039 issue: 3 year: 2020 ident: 10.1016/j.jfranklin.2022.05.023_bib0040 article-title: A numerical solution of a class of periodic coupled matrix equations publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2020.11.022 – volume: 47 start-page: 1813 issue: 8 year: 2011 ident: 10.1016/j.jfranklin.2022.05.023_bib0001 article-title: Stability and stabilization of discrete-time periodic linear systems with actuator saturation publication-title: Automatica doi: 10.1016/j.automatica.2011.04.015 – volume: 33 start-page: 1189 issue: 7 year: 2019 ident: 10.1016/j.jfranklin.2022.05.023_bib0027 article-title: The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle publication-title: Int. J. Adapt Control Signal Process. doi: 10.1002/acs.3029 |
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