Diffuse Algorithms for Neural and Neuro-Fuzzy Networks: With Applications in Control Engineering and Signal Processing presents new approaches to training neural and neuro-fuzzy networks. This book is divided into six chapters. Chapter 1 consists of plants models reviews, problems statements, and known results that are relevant to the subject matter of this book. Chapter 2 considers the RLS behavior on a finite interval. The theoretical results are illustrated by examples of solving problems of identification, control, and signal processing.
Properties of the bias, the matrix of second-order moments and the normalized average squared error of the RLS algorithm on a finite time interval are studied in Chapter 3. Chapter 4 deals with the problem of multilayer neural and neuro-fuzzy networks training with simultaneous estimation of the hidden and output layers parameters. The theoretical results are illustrated with the examples of pattern recognition, identification of nonlinear static, and dynamic plants.
Chapter 5 considers the estimation problem of the state and the parameters of the discrete dynamic plants in the absence of a priori statistical information about initial conditions or its incompletion. The Kalman filter and the extended Kalman filter diffuse analogues are obtained. Finally, Chapter 6 provides examples of the use of diffuse algorithms for solving problems in various engineering applications. This book is ideal for researchers and graduate students in control, signal processing, and machine learning.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Diffuse Algorithms for Estimating Parameters of Linear Regression - p. 17 3. Abstract - p. 17 4. 2.1 Problem Statement - p. 17 5. 2.2 Soft and Diffuse Initializations - p. 20 6. 2.3 Examples of Application - p. 39 7. Chapter 3. Statistical Analysis of Fluctuations of Least Squares Algorithm on Finite Time Interval - p. 49 8. Abstract - p. 49 9. 3.1 Problem Statement - p. 49 10. 3.2 Properties of Normalized Root Mean Square Estimation Error - p. 50 11. 3.3 Fluctuations of Estimates Under Soft Initialization with Large Parameters - p. 65 12. 3.4 Fluctuations Under Diffuse Initialization - p. 71 13. 3.5 Fluctuations with Random Inputs - p. 77 14. Chapter 4. Diffuse Neural and Neuro-Fuzzy Networks Training Algorithms - p. 80 15. Abstract - p. 80 16. 4.1 Problem Statement - p. 80 17. 4.2 Training With the Use of Soft and Diffuse Initializations - p. 82 18. 4.3 Training in the Absence of a Priori Information About Parameters of the Output Layer - p. 95 19. 4.4 Convergence of Diffuse Training Algorithms - p. 103 20. 4.5 Iterative Versions of Diffuse Training Algorithms - p. 123 21. 4.6 Diffuse Training Algorithm of Recurrent Neural Network - p. 125 22. 4.7 Analysis of Training Algorithms With Small Noise Measurements - p. 127 23. 4.8 Examples of Application - p. 130 24. Chapter 5. Diffuse Kalman Filter - p. 142 25. Abstract - p. 142 26. 5.1 Problem Statement - p. 142 27. 5.2 Estimation With Diffuse Initialization - p. 144 28. 5.3 Estimation in the Absence or Incomplete a Priori Information About Initial Conditions - p. 153 29. 5.4 Systems State Recovery in a Finite Number of Steps - p. 165 30. 5.5 Filtering With the Sliding Window - p. 166 31. 5.6 Diffuse Analog of the Extended Kalman Filter - p. 169 32. 5.7 Recurrent Neural Network Training - p. 170 33. 5.8 Systems With Partly Unknown Dynamics - p. 173 34. Chapter 6. Applications of Diffuse Algorithms - p. 175 35. Glossary - p. 193 36. References - p. 195 37. Index - p. 199
Diffuse Algorithms for Neural and Neuro-Fuzzy Networks: With Applications in Control Engineering and Signal Processing presents new approaches to training neural and neuro-fuzzy networks. This book is divided into six chapters. Chapter 1 consists of plants models reviews, problems statements, and known results that are relevant to the subject matter of this book. Chapter 2 considers the RLS behavior on a finite interval. The theoretical results are illustrated by examples of solving problems of identification, control, and signal processing.
Properties of the bias, the matrix of second-order moments and the normalized average squared error of the RLS algorithm on a finite time interval are studied in Chapter 3. Chapter 4 deals with the problem of multilayer neural and neuro-fuzzy networks training with simultaneous estimation of the hidden and output layers parameters. The theoretical results are illustrated with the examples of pattern recognition, identification of nonlinear static, and dynamic plants.
Chapter 5 considers the estimation problem of the state and the parameters of the discrete dynamic plants in the absence of a priori statistical information about initial conditions or its incompletion. The Kalman filter and the extended Kalman filter diffuse analogues are obtained. Finally, Chapter 6 provides examples of the use of diffuse algorithms for solving problems in various engineering applications. This book is ideal for researchers and graduate students in control, signal processing, and machine learning.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Diffuse Algorithms for Estimating Parameters of Linear Regression - p. 17 3. Abstract - p. 17 4. 2.1 Problem Statement - p. 17 5. 2.2 Soft and Diffuse Initializations - p. 20 6. 2.3 Examples of Application - p. 39 7. Chapter 3. Statistical Analysis of Fluctuations of Least Squares Algorithm on Finite Time Interval - p. 49 8. Abstract - p. 49 9. 3.1 Problem Statement - p. 49 10. 3.2 Properties of Normalized Root Mean Square Estimation Error - p. 50 11. 3.3 Fluctuations of Estimates Under Soft Initialization with Large Parameters - p. 65 12. 3.4 Fluctuations Under Diffuse Initialization - p. 71 13. 3.5 Fluctuations with Random Inputs - p. 77 14. Chapter 4. Diffuse Neural and Neuro-Fuzzy Networks Training Algorithms - p. 80 15. Abstract - p. 80 16. 4.1 Problem Statement - p. 80 17. 4.2 Training With the Use of Soft and Diffuse Initializations - p. 82 18. 4.3 Training in the Absence of a Priori Information About Parameters of the Output Layer - p. 95 19. 4.4 Convergence of Diffuse Training Algorithms - p. 103 20. 4.5 Iterative Versions of Diffuse Training Algorithms - p. 123 21. 4.6 Diffuse Training Algorithm of Recurrent Neural Network - p. 125 22. 4.7 Analysis of Training Algorithms With Small Noise Measurements - p. 127 23. 4.8 Examples of Application - p. 130 24. Chapter 5. Diffuse Kalman Filter - p. 142 25. Abstract - p. 142 26. 5.1 Problem Statement - p. 142 27. 5.2 Estimation With Diffuse Initialization - p. 144 28. 5.3 Estimation in the Absence or Incomplete a Priori Information About Initial Conditions - p. 153 29. 5.4 Systems State Recovery in a Finite Number of Steps - p. 165 30. 5.5 Filtering With the Sliding Window - p. 166 31. 5.6 Diffuse Analog of the Extended Kalman Filter - p. 169 32. 5.7 Recurrent Neural Network Training - p. 170 33. 5.8 Systems With Partly Unknown Dynamics - p. 173 34. Chapter 6. Applications of Diffuse Algorithms - p. 175 35. Glossary - p. 193 36. References - p. 195 37. Index - p. 199
