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[null,"1.","Record Nr.",null,"UNINA9910678005903321"]
[null,null,"Autore",null,"Xiao Lin"]
[null,null,"Titolo",null,"Zeroing neural networks : finite-time convergence design, analysis and applications / / Lin Xiao and Lei Jia"]
[null,null,"Pubbl/distr/stampa",null,"Piscataway, New Jersey ; ; Hoboken, New Jersey : , : IEEE Press : , : Wiley, , [2023]"]
[{"$nulls":4},"©2023"]
[null,null,"ISBN",null,"1-119-98604-4"]
[{"$nulls":4},"1-119-98602-8"]
[{"$nulls":4},"1-119-98603-6"]
[null,null,"Descrizione fisica",null,"1 online resource (435 pages)"]
[null,null,"Disciplina",null,"006.32"]
[null,null,"Soggetti",null,"Neural networks (Computer science)"]
[{"$nulls":4},"Nonlinear difference equations"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[{"$nulls":3},"Livello bibliografico","Monografia"]
[{"$nulls":3},"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Cover -- Title Page -- Copyright -- Contents -- List of Figures -- List of Tables -- Author Biographies -- Preface -- Acknowledgments -- Part I Application to Matrix Square Root -- Chapter 1 FTZNN for Time‐varying Matrix Square Root -- 1.1 Introduction -- 1.2 Problem Formulation and ZNN Model -- 1.3 FTZNN Model -- 1.3.1 Model Design -- 1.3.2 Theoretical Analysis -- 1.4 Illustrative Verification -- 1.5 Chapter Summary -- References -- Chapter 2 FTZNN for Static Matrix Square Root -- 2.1 Introduction -- 2.2 Solution Models -- 2.2.1 OZNN Model -- 2.2.2 FTZNN Model -- 2.3 Illustrative Verification -- 2.3.1 Example 1 -- 2.3.2 Example 2 -- 2.4 Chapter Summary -- References -- Part II Application to Matrix Inversion -- Chapter 3 Design Scheme I of FTZNN -- 3.1 Introduction -- 3.2 Problem Formulation and Preliminaries -- 3.3 FTZNN Model -- 3.3.1 Model Design -- 3.3.2 Theoretical Analysis -- 3.4 Illustrative Verification -- 3.4.1 Example 1: Nonrandom Time‐varying Coefficients -- 3.4.2 Example 2: Random Time‐varying Coefficients -- 3.5 Chapter Summary -- References -- Chapter 4 Design Scheme II of FTZNN -- 4.1 Introduction -- 4.2 Preliminaries -- 4.2.1 Mathematical Preparation -- 4.2.2 Problem Formulation -- 4.3 NT‐FTZNN Model -- 4.4 Theoretical Analysis -- 4.4.1 NT‐FTZNN in the Absence of Noises -- 4.4.2 NT‐FTZNN in the Presence of Noises -- 4.4.2.1 Dynamic Bounded "]
[{"$nulls":4},"Gradually Disappearing Noise -- 4.4.2.2 Dynamic Bounded Non‐disappearing Noise -- 4.5 Illustrative Verification -- 4.5.1 Example 1: Two‐dimensional Coefficient -- 4.5.2 Example 2: Six‐dimensional Coefficient -- 4.5.3 Example 3: Application to Mobile Manipulator -- 4.5.4 Example 4: Physical Comparative Experiments -- 4.6 Chapter Summary -- References -- Chapter 5 Design Scheme III of FTZNN -- 5.1 Introduction -- 5.2 Problem Formulation and Neural Solver -- 5.2.1 FPZNN Model."]
[{"$nulls":4},"5.2.2 IVP‐FTZNN Model -- 5.3 Theoretical Analysis -- 5.4 Illustrative Verification -- 5.4.1 Example 1: Two‐Dimensional Coefficient -- 5.4.2 Example 2: Three‐Dimensional Coefficient -- 5.5 Chapter Summary -- References -- Part III Application to Linear Matrix Equation -- Chapter 6 Design Scheme I of FTZNN -- 6.1 Introduction -- 6.2 Convergence Speed and Robustness Co‐design -- 6.3 R‐FTZNN Model -- 6.3.1 Design of R‐FTZNN -- 6.3.2 Analysis of R‐FTZNN -- 6.4 Illustrative Verification -- 6.4.1 Numerical Example -- 6.4.1.1 No Noise Considered -- 6.4.1.2 With Noises Considered -- 6.4.2 Applications: Robotic Motion Tracking -- 6.5 Chapter Summary -- References -- Chapter 7 Design Scheme II of FTZNN -- 7.1 Introduction -- 7.2 Problem Formulation -- 7.3 FTZNN Model -- 7.4 Theoretical Analysis -- 7.4.1 Convergence -- 7.4.2 Robustness -- 7.5 Illustrative Verification -- 7.5.1 Convergence -- 7.5.2 Robustness -- 7.6 Chapter Summary -- References -- Part IV Application to Optimization -- Chapter 8 FTZNN for Constrained Quadratic Programming -- 8.1 Introduction -- 8.2 Preliminaries -- 8.2.1 Problem Formulation -- 8.2.2 Optimization Theory -- 8.3 U‐FTZNN Model -- 8.4 Convergence Analysis -- 8.5 Robustness Analysis -- 8.6 Illustrative Verification -- 8.6.1 Qualitative Experiments -- 8.6.2 Quantitative Experiments -- 8.7 Application to Image Fusion -- 8.8 Application to Robot Control -- 8.9 Chapter Summary -- References -- Chapter 9 FTZNN for Nonlinear Minimization -- 9.1 Introduction -- 9.2 Problem Formulation and ZNN Models -- 9.2.1 Problem Formulation -- 9.2.2 ZNN Model -- 9.2.3 RZNN Model -- 9.3 Design and Analysis of R‐FTZNN -- 9.3.1 Second‐Order Nonlinear Formula -- 9.3.2 R‐FTZNN Model -- 9.4 Illustrative Verification -- 9.4.1 Constant Noise -- 9.4.2 Dynamic Noise -- 9.5 Chapter Summary -- References -- Chapter 10 FTZNN for Quadratic Optimization."]
[{"$nulls":4},"10.1 Introduction -- 10.2 Problem Formulation -- 10.3 Related Work: GNN and ZNN Models -- 10.3.1 GNN Model -- 10.3.2 ZNN Model -- 10.4 N‐FTZNN Model -- 10.4.1 Models Comparison -- 10.4.2 Finite‐Time Convergence -- 10.5 Illustrative Verification -- 10.6 Chapter Summary -- References -- Part V Application to the Lyapunov Equation -- Chapter 11 Design Scheme I of FTZNN -- 11.1 Introduction -- 11.2 Problem Formulation and Related Work -- 11.2.1 GNN Model -- 11.2.2 ZNN Model -- 11.3 FTZNN Model -- 11.4 Illustrative Verification -- 11.5 Chapter Summary -- References -- Chapter 12 Design Scheme II of FTZNN -- 12.1 Introduction -- 12.2 Problem Formulation and Preliminaries -- 12.3 FTZNN Model -- 12.3.1 Design of FTZNN -- 12.3.2 Analysis of FTZNN -- 12.4 Illustrative Verification -- 12.5 Application to Tracking Control -- 12.6 Chapter Summary -- References -- Chapter 13 Design Scheme III of FTZNN -- 13.1 Introduction -- 13.2 N‐FTZNN Model -- 13.2.1 Design of N‐FTZNN -- 13.2.2 Re‐Interpretation from Nonlinear PID Perspective -- 13.3 Theoretical Analysis -- 13.4 Illustrative Verification -- 13.4.1 Numerical Comparison -- 13.4.2 Application Comparison -- 13.4.3 Experimental Verification -- 13.5 Chapter Summary -- References -- Part VI Application to the Sylvester Equation -- Chapter 14 Design Scheme I of FTZNN -- 14.1 Introduction -- 14.2 Problem Formulation "]
[{"$nulls":4},"and ZNN Model -- 14.3 N‐FTZNN Model -- 14.3.1 Design of N‐FTZNN -- 14.3.2 Theoretical Analysis -- 14.4 Illustrative Verification -- 14.5 Robotic Application -- 14.6 Chapter Summary -- References -- Chapter 15 Design Scheme II of FTZNN -- 15.1 Introduction -- 15.2 ZNN Model and Activation Functions -- 15.2.1 ZNN Model -- 15.2.2 Commonly Used AFs -- 15.2.3 Two Novel Nonlinear AFs -- 15.3 NT‐PTZNN Models and Theoretical Analysis -- 15.3.1 NT‐PTZNN1 Model -- 15.3.1.1 Case 1 -- 15.3.1.2 Case 2."]
[{"$nulls":4},"15.3.2 NT‐PTZNN2 Model -- 15.3.2.1 Case 1 -- 15.3.2.2 Case 2 -- 15.4 Illustrative Verification -- 15.4.1 Example 1 -- 15.4.2 Example 2 -- 15.4.3 Example 3 -- 15.5 Chapter Summary -- References -- Chapter 16 Design Scheme III of FTZNN -- 16.1 Introduction -- 16.2 ZNN Model and Activation Function -- 16.2.1 ZNN Model -- 16.2.2 Sign‐bi‐power Activation Function -- 16.3 FTZNN Models with Adaptive Coefficients -- 16.3.1 SA‐FTZNN Model -- 16.3.2 PA‐FTZNN Model -- 16.3.3 EA‐FTZNN Model -- 16.4 Illustrative Verification -- 16.5 Chapter Summary -- References -- Part VII Application to Inequality -- Chapter 17 Design Scheme I of FTZNN -- 17.1 Introduction -- 17.2 FTZNN Models Design -- 17.2.1 Problem Formulation -- 17.2.2 ZNN Model -- 17.2.3 Vectorization -- 17.2.4 Activation Functions -- 17.2.5 FTZNN Models -- 17.3 Theoretical Analysis -- 17.3.1 Global Convergence -- 17.3.2 Finite‐Time Convergence -- 17.4 Illustrative Verification -- 17.5 Chapter Summary -- References -- Chapter 18 Design Scheme II of FTZNN -- 18.1 Introduction -- 18.2 NT‐FTZNN Model Deisgn -- 18.2.1 Problem Formulation -- 18.2.2 ZNN Model -- 18.2.3 NT‐FTZNN Model -- 18.2.4 Activation Functions -- 18.3 Theoretical Analysis -- 18.3.1 Global Convergence -- 18.3.2 Finite‐Time Convergence -- 18.3.3 Noise‐Tolerant Convergence -- 18.4 Illustrative Verification -- 18.5 Chapter Summary -- References -- Part VIII Application to Nonlinear Equation -- Chapter 19 Design Scheme I of FTZNN -- 19.1 Introduction -- 19.2 Model Formulation -- 19.2.1 OZNN Model -- 19.2.2 FTZNN Model -- 19.2.3 Models Comparison -- 19.3 Convergence Analysis -- 19.4 Illustrative Verification -- 19.4.1 Nonlinear Equation f(u) with Simple Root -- 19.4.2 Nonlinear Equation f(u) with Multiple Root -- 19.5 Chapter Summary -- References -- Chapter 20 Design Scheme II of FTZNN -- 20.1 Introduction -- 20.2 Problem and Model Formulation."]
[{"$nulls":4},"20.2.1 GNN Model -- 20.2.2 OZNN Model -- 20.3 FTZNN Model and Finite‐Time Convergence -- 20.4 Illustrative Verification -- 20.5 Chapter Summary -- References -- Chapter 21 Design Scheme III of FTZNN -- 21.1 Introduction -- 21.2 Problem Formulation and ZNN Models -- 21.2.1 Problem Formulation -- 21.2.2 ZNN Model -- 21.3 Robust and Fixed‐Time ZNN Model -- 21.4 Theoretical Analysis -- 21.4.1 Case 1: No Noise -- 21.4.2 Case 2: Under External Noises -- 21.5 Illustrative Verification -- 21.6 Chapter Summary -- References -- Index -- EULA."]