1 Introduction 1
1.1 Neural Network Control 1
1.1.1 Why Neural Network Control? 1
1.1.2 Review of Neural Network Control 2
1.1.3 Review of RBF Adaptive Control 3
1.2 Review of RBF Neural Network 3
1.3 RBF Adaptive Control for Robot Manipulators 4
1.4 S Function Design for Control System 5
1.4.1 S Function Introduction 5
1.4.2 Basic Parameters in S Function 5
1.4.3 Examples 6
1.5 An Example of a Simple Adaptive Control System 7
1.5.1 System Description 7
1.5.2 Adaptive Control Law Design 7
1.5.3 Simulation Example 9
Appendix 11
References 15
2 RBF Neural Network Design and Simulation 19
2.1 RBF Neural Network Design and Simulation 19
2.1.1 RBF Algorithm 19
2.1.2 RBF Design Example with Matlab Simulation 20
2.2 RBF Neural Network Approximation Based on Gradient Descent Method 22
2.2.1 RBF Neural Network Approximation 22
2.2.2 Simulation Example 24
2.3 Effect of Gaussian Function Parameters on RBF Approximation 25
2.4 Effect of Hidden Nets Number on RBF Approximation 28
2.5 RBF Neural Network Training for System Modeling 33
2.5.1 RBF Neural Network Training 33
2.5.2 Simulation Example 34
2.6 RBF Neural Network Approximation 36
Appendix 37
References 53
3 RBF Neural Network Control Based on Gradient Descent Algorithm 55
3.1 Supervisory Control Based on RBF Neural Network 55
3.1.1 RBF Supervisory Control 55
3.1.2 Simulation Example 56
3.2 RBFNN-Based Model Reference Adaptive Control 58
3.2.1 Controller Design 58
3.2.2 Simulation Example 59
3.3 RBF Self-Adjust Control 61
3.3.1 System Description 61
3.3.2 RBF Controller Design 61
3.3.3 Simulation Example 63
Appendix 63
References 69
4 Adaptive RBF Neural Network Control 71
4.1 Adaptive Control Based on Neural Approximation 71
4.1.1 Problem Description 71
4.1.2 Adaptive RBF Controller Design 72
4.1.3 Simulation Examples 75
4.2 Adaptive Control Based on Neural Approximation with Unknown Parameter 79
4.2.1 Problem Description 79
4.2.2 Adaptive Controller Design 79
4.2.3 Simulation Examples 83
4.3 A Direct Method for Robust Adaptive Control by RBF 83
4.3.1 System Description 83
4.3.2 Desired Feedback Control and Function Approximation 86
4.3.3 Controller Design and Performance Analysis 87
4.3.4 Simulation Example 90
Appendix 92
References 112
5 Neural Network Sliding Mode Control 113
5.1 Typical Sliding Mode Controller Design 114
5.2 Sliding Mode Control Based on RBF for Second-Order SISO Nonlinear System 116
5.2.1 Problem Description 116
5.2.2 Sliding Mode Control Based on RBF for Unknown f(·) 117
5.2.3 Simulation Example 118
5.3 Sliding Mode Control Based on RBF for Unknown f(·) and g(·) 120
5.3.1 Introduction 120
5.3.2 Simulation Example 122
Appendix 123
References 132
6 Adaptive RBF Control Based on Global Approximation 133
6.1 Adaptive Control with RBF Neural Network Compensation for Robotic Manipulators 134
6.1.1 Problem Description 134
6.1.2 RBF Approximation 135
6.1.3 RBF Controller and Adaptive Law Design and Analysis 136
6.1.4 Simulation Examples 140
6.2 RBF Neural Robot Controller Design with Sliding Mode Robust Term 144
6.2.1 Problem Description 144
6.2.2 RBF Approximation 147
6.2.3 Control Law Design and Stability Analysis 147
6.2.4 Simulation Examples 148
6.3 Robust Control Based on RBF Neural Network with HJI 153
6.3.1 Foundation 153
6.3.2 Controller Design and Analysis 153
6.3.3 Simulation Examples 156
Appendix 159
References 191
7 Adaptive Robust RBF Control Based on Local Approximation 193
7.1 Robust Control Based on Nominal Model for Robotic Manipulators 193
7.1.1 Problem Description 193
7.1.2 Controller Design 194
7.1.3 Stability Analysis 195
7.1.4 Simulation Example 196
7.2 Adaptive RBF Control Based on Local Model Approximation for Robotic Manipulators 197
7.2.1 Problem Description 197
7.2.2 Controller Design 199
7.2.3 Stability Analysis 200
7.2.4 Simulation Examples 203
7.3 Adaptive Neural Network Control of Robot Manipulators in Task Space 205
7.3.1 Coordination Transformation from Task Space to Joint Space 208
7.3.2 Neural Network Modeling of Robot Manipulators 208
7.3.3 Controller Design 210
7.3.4 Simulation Examples 213
Appendix 217
References 249
8 Backstepping Control with RBF 251
8.1 Introduction 251
8.2 Backstepping Control for Inverted Pendulum 252
8.2.1 System Description 253
8.2.2 Controller Design 253
8.2.3 Simulation Example 254
8.3 Backstepping Control Based on RBF for Inverted Pendulum 255
8.3.1 System Description 255
8.3.2 Backstepping Controller Design 256
8.3.3 Adaptive Law Design 257
8.3.4 Simulation Example 259
8.4 Backstepping Control for Single-Link Flexible Joint Robot 260
8.4.1 System Description 260
8.4.2 Backstepping Controller Design 262
8.5 Adaptive Backstepping Control with RBF for Single-Link Flexible Joint Robot 265
8.5.1 Backstepping Controller Design with Function Estimation 265
8.5.2 Backstepping Controller Design with RBF Approximation 269
8.5.3 Simulation Examples 272
Appendix 276
References 291
9 Digital RBF Neural Network Control 293
9.1 Adaptive Runge-Kutta-Merson Method 293
9.1.1 Introduction 293
9.1.2 Simulation Example 295
9.2 Digital Adaptive Control for SISO System 295
9.2.1 Introduction 295
9.2.2 Simulation Example 297
9.3 Digital Adaptive RBF Control for Two-Link Manipulators 298
9.3.1 Introduction 298
9.3.2 Simulation Example 299
Appendix 299
References 309
10 Discrete Neural Network Control 311
10.1 Introduction 311
10.2 Direct RBF Control for a Class of Discrete-Time Nonlinear System 312
10.2.1 System Description 312
10.2.2 Controller Design and Stability Analysis 312
10.2.3 Simulation Examples 316
10.3 Adaptive RBF Control for a Class of Discrete-Time Nonlinear System 319
10.3.1 System Description 319
10.3.2 Traditional Controller Design 320
10.3.3 Adaptive Neural Network Controller Design 320
10.3.4 Stability Analysis 322
10.3.5 Simulation Examples 324
Appendix 329
References 337
11 Adaptive RBF Observer Design and Sliding Mode Control 339
11.1 Adaptive RBF Observer Design 339
11.1.1 System Description 339
11.1.2 Adaptive RBF Observer Design and Analysis 340
11.1.3 Simulation Examples 343
11.2 Sliding Mode Control Based on RBF Adaptive Observer 347
11.2.1 Sliding Mode Controller Design 347
11.2.2 Simulation Example 349
Appendix 351
References 362
Index 363