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