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by Jose C. Principe, Danilo Comminiello
Adaptive Learning Methods for Nonlinear System Modeling
Cover image
Title page
Table of Contents
Copyright
Contributors
Preface
Acknowledgments
Chapter 1: Introduction
Abstract
1.1. Nonlinear System Modeling: Background, Motivation and Opportunities
1.2. Key Factors in Defining Adaptive Learning Methods for Nonlinear System Modeling
1.3. Book Organization
1.4. Further Readings
References
Part 1: Linear-in-the-Parameters Nonlinear Filters
Chapter 2: Orthogonal LIP Nonlinear Filters
Abstract
2.1. Introduction
2.2. LIP Nonlinear Filters
2.3. Recent Identification Methods for Orthogonal Filters
2.4. Experimental Results
2.5. Concluding Remarks
References
Chapter 3: Spline Adaptive Filters
Abstract
Acknowledgements
3.1. Introduction
3.2. Foundation of Spline Interpolation
3.3. Spline Adaptive Filters
3.4. Convergence Properties
3.5. Experimental Results
3.6. Conclusion
References
Chapter 4: Recent Advances on LIP Nonlinear Filters and Their Applications
Abstract
Acknowledgements
4.1. Introduction
4.2. A Concise Categorization of State-of-the-Art LIP Nonlinear Filters
4.3. Fundamental Methods for Coefficient Adaptation
4.4. Significance-Aware Filtering
4.5. Experiments and Evaluation
4.6. Outlook on Model Structure Estimation
4.7. Summary
References
Part 2: Adaptive Algorithms in the Reproducing Kernel Hilbert Space
Chapter 5: Maximum Correntropy Criterion–Based Kernel Adaptive Filters
Abstract
5.1. Introduction
5.2. Kernel Adaptive Filters
5.3. Maximum Correntropy Criterion
5.4. Kernel Adaptive Filters Under Generalized MCC
5.5. Simulation Results
5.6. Conclusion
References
Chapter 6: Kernel Subspace Learning for Pattern Classification
Abstract
6.1. Introduction
6.2. Kernel Methods
6.3. Kernel Subspace Approximation
6.4. Adaptive Kernel Subspace Approximation Algorithm
6.5. Infrastructures
6.6. Conclusion
Appendix 6.A.
References
Chapter 7: A Random Fourier Features Perspective of KAFs With Application to Distributed Learning Over Networks
Abstract
7.1. Introduction
7.2. Approximating the Kernel
7.3. Online Kernel-Based Learning: A Random Fourier Features Perspective
7.4. Online Distributed Learning With Kernels
7.5. Conclusions
References
Chapter 8: Kernel-Based Inference of Functions Over Graphs
Abstract
Acknowledgements
8.1. Introduction
8.2. Reconstruction of Functions Over Graphs
8.3. Inference of Dynamic Functions Over Dynamic Graphs
References
Part 3: Nonlinear Modeling With Multiple Learning Machines
Chapter 9: Online Nonlinear Modeling via Self-Organizing Trees
Abstract
Acknowledgements
9.1. Introduction
9.2. Self-Organizing Trees for Regression Problems
9.3. Self-Organizing Trees for Binary Classification Problems
9.4. Numerical Results
Appendix 9.A.
References
Chapter 10: Adaptation and Learning Over Networks for Nonlinear System Modeling
Abstract
Acknowledgements
10.1. Introduction
10.2. Mathematical Formulation of the Problem
10.3. Existing Approaches to Nonlinear Distributed Filtering
10.4. A Distributed Kernel Filter for Multitask Problems
10.5. Experimental Evaluation
10.6. Discussion and Open Problems
References
Chapter 11: Combined Filtering Architectures for Complex Nonlinear Systems
Abstract
11.1. Introduction
11.2. Nonlinear Adaptive Filters
11.3. Different Approaches to Combine Nonlinear Adaptive Filters
11.4. Combined Nonlinear Filters With Diversity in the Parameters
11.5. Combination Schemes to Simplify the Selection of the Filter Structure
11.6. Conclusions
References
Part 4: Nonlinear Modeling by Neural Systems
Chapter 12: Echo State Networks for Multidimensional Data: Exploiting Noncircularity and Widely Linear Models
Abstract
Acknowledgements
12.1. Introduction
12.2. Mathematical Background
12.3. Quaternion ESNs
12.4. Simulations
12.5. Discussion and Conclusion
References
Chapter 13: Identification of Short-Term and Long-Term Functional Synaptic Plasticity From Spiking Activities
Abstract
Acknowledgements
13.1. Introduction
13.2. Identification of STSP With Nonlinear Dynamical Model
13.3. Identification of LTSP With Nonstationary Model
13.4. Identification of Synaptic Learning Rule
13.5. Summary and Discussion
References
Chapter 14: Adaptive H∞ Tracking Control of Nonlinear Systems Using Reinforcement Learning
Abstract
14.1. Introduction
14.2. H∞ Optimal Tracking Control for Nonlinear Affine Systems
14.3. H∞ Optimal Tracking Control for a Class of Nonlinear Nonaffine Systems
References
Chapter 15: Adaptive Dynamic Programming for Optimal Control of Nonlinear Distributed Parameter Systems
Abstract
Acknowledgements
15.1. Introduction
15.2. Problem Description
15.3. Model Reduction Based on KLD and Singular Perturbation Technique
15.4. Adaptive Optimal Control Design With NDP
15.5. Adaptive Optimal Control Based on Policy Iteration for Partially Unknown DPSs
15.6. Conclusions
References
Index
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