Competition-Based Neural Networks with Robotic Applications (eBook)

Preface 7
Acknowledgements 11
Contents 12
1 Competition Aided with Discrete-Time Dynamic Feedback 15
1.1 Introduction 15
1.2 Problem Definition 16
1.3 Model Formulation 16
1.4 Theoretical Results 17
1.5 Illustrative Examples 20
1.5.1 Discrete-Time Static Competition 20
1.5.2 Discrete-Time Dynamic Competition 23
1.6 Summary 23
References 24
2 Competition Aided with Continuous-Time Nonlinear Model 27
2.1 Introduction 27
2.2 The Model 28
2.3 Theoretical Analysis and Results 29
2.4 Illustrative Examples 32
2.4.1 Static Competition 32
2.4.2 Dynamic Competition 34
2.5 Summary 36
References 36
3 Competition Aided with Finite-Time Neural Network 38
3.1 Introduction 38
3.2 Model Description 39
3.3 Convergence Analysis 43
3.4 An Illustrative Example 49
3.4.1 Accuracy 49
3.4.2 Convergence Speed 52
3.4.3 Comparisons on Computational Efficiency in Numerical Simulations 53
3.4.4 Sensitivity to Additive Noise 54
3.4.5 Robustness Against Time Delay 54
3.4.6 Discussion 57
3.5 Solving k-WTA with the Proposed Neural Network 60
3.5.1 Quadratic Programming Formulation for k-TWA 60
3.5.2 Theoretical Results for Solving k-WTA with the Proposed Neural Network 63
3.5.3 k-WTA Simulations 65
3.6 Summary 67
References 67
4 Competition Based on Selective Positive-Negative Feedback 69
4.1 Introduction 69
4.2 Preliminaries 71
4.3 The Winner-Take-All Neural Network 72
4.3.1 The Neural Network Based Winner-Take-All Problem 72
4.3.2 Neuro-Dynamics 73
4.4 Convergence Results 74
4.5 Discussion on One-Sided Competition Versus Closely-Matched Competition 79
4.6 Simulation Examples 79
4.6.1 Static Competition 80
4.6.2 Dynamic Competition 88
4.7 Summary 88
References 89
5 Distributed Competition in Dynamic Networks 92
5.1 Introduction 92
5.2 Problem Definition: Distributed WTA on Graphs 94
5.3 Distributed WTA Protocol 95
5.3.1 Basic Properties 96
5.4 Convergence Analysis 97
5.4.1 Global Convergence to the Equilibrium Point Set 97
5.4.2 Instability of Non-WTA Solutions 102
5.4.3 Global Stability of the WTA Solution 104
5.5 Numerical Validation 106
5.6 Summary 110
References 111
6 Competition-Based Distributed Coordination Control of Robots 114
6.1 Introduction 114
6.2 Preliminary and Problem Formulation 116
6.2.1 Redundant Robot Manipulator 117
6.2.2 Problem Definitions and Assumptions 118
6.3 Dynamic Task Allocation with Limited Communications 119
6.4 Illustrative Example 126
6.5 Summary 130
References 131