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Zeroing Neural Networks

E-BookEPUB2 - DRM Adobe / EPUBE-Book
432 Seiten
Englisch
John Wiley & Sonserschienen am02.02.20231. Auflage
Zeroing Neural Networks
Describes the theoretical and practical aspects of finite-time ZNN methods for solving an array of computational problems
Zeroing Neural Networks (ZNN) have become essential tools for solving discretized sensor-driven time-varying matrix problems in engineering, control theory, and on-chip applications for robots. Building on the original ZNN model, finite-time zeroing neural networks (FTZNN) enable efficient, accurate, and predictive real-time computations. Setting up discretized FTZNN algorithms for different time-varying matrix problems requires distinct steps.
Zeroing Neural Networks provides in-depth information on the finite-time convergence of ZNN models in solving computational problems. Divided into eight parts, this comprehensive resource covers modeling methods, theoretical analysis, computer simulations, nonlinear activation functions, and more. Each part focuses on a specific type of time-varying computational problem, such as the application of FTZNN to the Lyapunov equation, linear matrix equation, and matrix inversion. Throughout the book, tables explain the performance of different models, while numerous illustrative examples clarify the advantages of each FTZNN method. In addition, the book: Describes how to design, analyze, and apply FTZNN models for solving computational problems
Presents multiple FTZNN models for solving time-varying computational problems
Details the noise-tolerance of FTZNN models to maximize the adaptability of FTZNN models to complex environments
Includes an introduction, problem description, design scheme, theoretical analysis, illustrative verification, application, and summary in every chapter

Zeroing Neural Networks: Finite-time Convergence Design, Analysis and Applications is an essential resource for scientists, researchers, academic lecturers, and postgraduates in the field, as well as a valuable reference for engineers and other practitioners working in neurocomputing and intelligent control.


LIN XIAO, PhD, is a Professor in the College of Information Science and Engineering at Hunan Normal University, Changsha, China. He has authored more than 100 papers in international conferences and journals, including IEEE-TCYB, IEEE-TII, IEEE-TSMCS. Professor Xiao is Associate Editor of IEEE-TNNLS.
LEI JIA is a PhD degree candidate in Operations Research and Control in the College of Mathematics and Statistics at Hunan Normal University, Changsha, China. She has authored or co-authored more than 20 scientific articles, including 13 IEEE-transaction papers.mehr
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Produkt

KlappentextZeroing Neural Networks
Describes the theoretical and practical aspects of finite-time ZNN methods for solving an array of computational problems
Zeroing Neural Networks (ZNN) have become essential tools for solving discretized sensor-driven time-varying matrix problems in engineering, control theory, and on-chip applications for robots. Building on the original ZNN model, finite-time zeroing neural networks (FTZNN) enable efficient, accurate, and predictive real-time computations. Setting up discretized FTZNN algorithms for different time-varying matrix problems requires distinct steps.
Zeroing Neural Networks provides in-depth information on the finite-time convergence of ZNN models in solving computational problems. Divided into eight parts, this comprehensive resource covers modeling methods, theoretical analysis, computer simulations, nonlinear activation functions, and more. Each part focuses on a specific type of time-varying computational problem, such as the application of FTZNN to the Lyapunov equation, linear matrix equation, and matrix inversion. Throughout the book, tables explain the performance of different models, while numerous illustrative examples clarify the advantages of each FTZNN method. In addition, the book: Describes how to design, analyze, and apply FTZNN models for solving computational problems
Presents multiple FTZNN models for solving time-varying computational problems
Details the noise-tolerance of FTZNN models to maximize the adaptability of FTZNN models to complex environments
Includes an introduction, problem description, design scheme, theoretical analysis, illustrative verification, application, and summary in every chapter

Zeroing Neural Networks: Finite-time Convergence Design, Analysis and Applications is an essential resource for scientists, researchers, academic lecturers, and postgraduates in the field, as well as a valuable reference for engineers and other practitioners working in neurocomputing and intelligent control.


LIN XIAO, PhD, is a Professor in the College of Information Science and Engineering at Hunan Normal University, Changsha, China. He has authored more than 100 papers in international conferences and journals, including IEEE-TCYB, IEEE-TII, IEEE-TSMCS. Professor Xiao is Associate Editor of IEEE-TNNLS.
LEI JIA is a PhD degree candidate in Operations Research and Control in the College of Mathematics and Statistics at Hunan Normal University, Changsha, China. She has authored or co-authored more than 20 scientific articles, including 13 IEEE-transaction papers.
Details
Weitere ISBN/GTIN9781119986034
ProduktartE-Book
EinbandartE-Book
FormatEPUB
Format Hinweis2 - DRM Adobe / EPUB
FormatFormat mit automatischem Seitenumbruch (reflowable)
Erscheinungsjahr2023
Erscheinungsdatum02.02.2023
Auflage1. Auflage
Seiten432 Seiten
SpracheEnglisch
Dateigrösse30304 Kbytes
Artikel-Nr.10202827
Rubriken
Genre9201

Inhalt/Kritik

Leseprobe

List of Figures
Figure 1.1 Transient behavior of synthesized by the OZNN model (1.5) starting with 10 randomly generated initial states, where solid curves correspond to neural state , and dash curves correspond to theoretical matrix square root . Figure 1.2 Transient behavior of synthesized by FTZNN model (1.13) starting with 10 randomly generated initial states, where solid curves correspond to neural state , and dash curves correspond to theoretical time-varying matrix square root . Figure 1.3 Transient behavior of the residual error corresponding to synthesized by the OZNN model (1.5) and FTZNN model (1.13). (a) By the OZNN model (1.5) and (b) by FTZNN model (1.13). Figure 2.1 Simulative results of OZNN model (2.3) using linear activation functions under the condition of and a randomly generated close to . (a) Transient behavior of state matrix and (b) transient behavior of residual error . Figure 2.2 Simulative results of OZNN model (2.3) using power-sigmoid activation functions under the condition of and a randomly generated close to . (a) Transient behavior of state matrix and (b) transient behavior of residual error . Figure 2.3 Simulative results of FTZNN model (2.5) under the condition of , and a randomly generated close to . (a) Transient behavior of state matrix and (b) transient behavior of residual error . Figure 2.4 Transient behavior of residual error synthesized by FTZNN model (2.5) under the condition of and a randomly generated close to . (a) With and (b) with . Figure 3.1 Transient behavior of synthesized by GNN model (3.2) starting with 8 randomly generated initial states under the condition of . Figure 3.2 Transient behavior of synthesized by OZNN model (3.3) starting with 8 randomly generated initial states under the condition of . Figure 3.3 Transient behavior of the residual error corresponding to synthesized by GNN model (3.2) and OZNN model (3.3). (a) By GNN model (3.2) and (b) by OZNN model (3.3). Figure 3.4 Transient behavior of synthesized by FTZNN model (3.11) starting with 8 randomly generated initial states under the conditions of . Figure 3.5 Transient behavior of the residual error synthesized by FTZNN model (3.11) under the conditions of . (a) and (b) . Figure 3.6 Transient behavior of the residual error synthesized by FTZNN model (3.11) under the conditions of . (a) and (b) . Figure 3.7 Transient behavior of the residual error synthesized by FTZNN model (3.11) using random time-varying coefficients under the conditions of . (a) and (b) . Figure 4.1 Transient behavior of NT-FTZNN model (4.6) activated by VAF for solving time-dependent matrix inversion (4.9) without noise. (a) State solutions and (b) residual error. Figure 4.2 Transient behavior of the ZNN model activated by LAF for solving time-dependent matrix inversion (4.9) with noise . (a) State solutions and (b) residual error. Figure 4.3 Transient behavior of the ZNN model activated by power-sum activation function (PSAF) for solving time-dependent matrix inversion (4.9) with noise . (a) State solutions and (b) residual error. Figure 4.4 Transient behavior of the ZNN model activated by SBPAF for solving time-dependent matrix inversion (4.9) with noise . (a) State solutions and (b) residual error. Figure 4.5 Transient behavior of NT-FTZNN model (4.6) activated by VAF for solving time-dependent matrix inversion (4.9) with noise . (a) State solutions and (b) residual error. Figure 4.6 Transient behavior of residual errors synthesized by NT-FTZNN model (4.6) activated by VAF and other ZNN models activated by different activation functions in different noise environments for solving time-dependent matrix inversion (4.9). (a) Noise with , (b) noise with , (c) noise with , and (d) noise with . Figure 4.7 Transient behavior of residual errors synthesized by NT-FTZNN model (4.6) activated by VAF and other ZNN models activated by different activation functions in different noise environments for solving time-dependent matrix inversion (4.9) with different values of parameter . (a) Noise with and (b) noise with . Figure 4.8 Transient behavior of residual errors synthesized by NT-FTZNN model (4.6) activated by VAF, GNN model, IEZNN model, and other ZNN models activated by LAF, PSAF, and SBPAF under different noise environments for solving time-dependent matrix inversion (4.11). (a) , (b) , and (c) . Figure 4.9 Circular task tracking synthesized by the original ZNN model activated by the SBP activation function in the presence of additive noise . (a) Whole tracking process, (b) task comparison, and (c) position error. Figure 4.10 Circular task tracking synthesized by NT-FTZNN model (4.6) in the presence of additive noise . (a) Whole tracking process, (b) task comparison, and (c) position error. Figure 4.11 Physical comparative experiments of a butterfly-path tracking task generated by different ZNN models and performed on the Kinova robot manipulator when disturbed by external noise. (a) Failure by SBPAF activated ZNN and (b) success by NT-FTZNN. Figure 5.1 Simulative results using FPZNN model (5.4) with SBPAF when solving TVMI (5.1) of Example 1 with . (a) State solution and (b) residual error . Figure 5.2 Simulative results using EVPZNN model (5.7) with SBPAF when solving TVMI (5.1) of Example 1 with . (a) State solution and (b) residual error . Figure 5.3 Simulative results using VPZNN model (5.9) with SBPAF when solving TVMI (5.1) of Example 1 with . (a) State solution and (b) residual error . Figure 5.4 Simulative results using IVP-FTZNN model (5.11) with SBPAF when solving TVMI (5.1) of Example 1 with . (a) State solution and (b) residual error . Figure 5.5 Residual errors of FPZNN (5.4), EVPZNN (5.7), VPZNN (5.9), and IVP-FTZNN (5.11) with SBPAF when solving TVMI (5.1) of Example 1 with . Figure 5.6 Residual errors of IVP-FTZNN model (5.11) with different activation functions when solving TVMI (5.1) of Example 1 with . Figure 5.7 Simulative results using IVP-FTZNN model (5.11) with SBPAF when solving TVMI (5.1) of Example 2 with . (a) State solution and (b) residual error . Figure 5.8 Simulative residual errors using FPZNN (5.4), EVPZNN (5.7), VPZNN (5.9), and IVP-FTZNN (5.11) with SBPAF when solving TVMI (5.1) of Example 2 with different and . (a) With , (b) with , (c) with , and (d) with . Figure 5.9 Simulative residual errors using FPZNN (5.4), EVPZNN (5.7), VPZNN (5.9), and IVP-FTZNN (5.11) with SBPAF when solving TVMI (5.1) of Example 2 with different , and noises . (a) With and , (b) with and , (c) with and , and (d) With and . Figure 5.10 Simulative residual errors using FPZNN (5.4), EVPZNN (5.7), VPZNN (5.9), and IVP-FTZNN (5.11) with SBPAF when solving TVMI (5.1) of Example 2 with and different noises . (a) With and with . Figure 6.1 Simulative results generated by the R-FTZNN model (6.26) for solving the time-varying linear equation system with no noise. (a) The first element of the neural state and the theoretical solution . (b) The second element of neural state and the theoretical solution . (c) The residual error corresponding to the neural state...mehr

Autor

LIN XIAO, PhD, is a Professor in the College of Information Science and Engineering at Hunan Normal University, Changsha, China. He has authored more than 100 papers in international conferences and journals, including IEEE-TCYB, IEEE-TII, IEEE-TSMCS. Professor Xiao is Associate Editor of IEEE-TNNLS.

LEI JIA is a PhD degree candidate in Operations Research and Control in the College of Mathematics and Statistics at Hunan Normal University, Changsha, China. She has authored or co-authored more than 20 scientific articles, including 13 IEEE-transaction papers.