Neural Network Control of Robot Manipulators and Non-Linear Systems

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
List of Tables of Design Equations......Page 12
List of Figures......Page 14
Series Introduction......Page 20
Preface......Page 22
1 Background on Neural Networks......Page 26
  1.1.1 Neuron Mathematical Model......Page 27
  1.1.2 Multilayer Perceptron......Page 32
  1.1.3 Linear-in-the-Parameter (LIP) Neural Nets......Page 35
  1.1.4 Dynamic Neural Networks......Page 39
 1.2 PROPERTIES OF NEURAL NETWORKS......Page 49
  1.2.1 Classification, Association, and Pattern Recognition......Page 50
  1.2.2 Function Approximation......Page 55
 1.3 NEURAL NETWORK WEIGHT SELECTION AND TRAINING......Page 57
  1.3.1 Direct Computation of the Weights......Page 58
  1.3.2 Training the One-Layer Neural Network- Gradient Descent......Page 60
  1.3.3 Training the Multilayer Neural Network- Backpropagation Tuning......Page 68
  1.3.4 Improvements on Gradient Descent......Page 78
  1.3.5 Hebbian Tuning......Page 81
  1.3.6 Continuous-Time Tuning......Page 82
 1.4 REFERENCES......Page 85
 1.5 PROBLEMS......Page 88
 2.1 DYNAMICAL SYSTEMS......Page 92
  2 .1.1 Continuous-Time Systems......Page 93
  2 .1. 2 Discrete-Time Systems......Page 96
  2.2.1 Vector and Matrix Norms......Page 100
  2.2.2 Continuity and Function Norms......Page 101
 2.3 PROPERTIES OF DYNAMICAL SYSTEMS......Page 102
  2.3.1 Stability......Page 103
  2.3.2 Passivity......Page 105
  2.3.3 Observability and Controllability......Page 108
 2.4 FEEDBACK LINEARIZATION AND CONTROL SYSTEM DESIGN......Page 111
  2.4.1 Input-Output Feedback Linearization Controllers......Page 112
  2.4.2 Computer Simulation of Feedback Control Systems......Page 117
  2.4.3 Feedback Linearization for Discrete-Time Systems......Page 121
  2.5.1 Lyapunov Analysis for Autonomous Systems......Page 122
  2.5.2 Controller Design Using Lyapunov Techniques......Page 128
  2.5.3 Lyapunov Analysis for Non-Autonomous Systems......Page 131
  2.5.4 Extensions of Lyapunov Techniques and Bounded Stability......Page 134
 2.6 REFERENCES......Page 140
 2.7 PROBLEMS......Page 141
 3.0.1 Commercial Robot Controllers......Page 148
 3.1 KINEMATICS AND JACOBIANS......Page 149
  3.1.1 Kinematics of Rigid Serial-Link Manipulators......Page 150
  3.1.2 Robot Jacobians......Page 153
 3.2 ROBOT DYNAMICS AND PROPERTIES......Page 154
  3.2.1 Joint Space Dynamics and Properties......Page 155
  3.2.2 State Variable Representations......Page 159
  3.2.3 Cartesian Dynamics and Actuator Dynamics......Page 160
  3.3.1 Computed-Torque (CT) Control......Page 161
  3.3.2 Computer Simulation of Robot Controllers......Page 163
  3.3.3 Approximate Computed-Torque Control and Classical Joint Control......Page 168
  3.3.4 Digital Control......Page 170
 3.4 FILTERED-ERROR APPROXIMATION-BASED CONTROL......Page 172
  3.4.1 A General Controller Design Framework Based on Approximation......Page 179
  3.4.3 Adaptive Control......Page 181
  3.4.4 Robust Control......Page 187
  3.4.5 Learning Control......Page 190
 3.5 CONCLUSIONS......Page 192
 3.6 REFERENCES......Page 193
 3.7 PROBLEMS......Page 194
4 Neural Network Robot Control......Page 198
 4.1 ROBOT ARM DYNAMICS AND TRACKING ERROR DYNAMICS......Page 201
 4.2 ONE-LAYER FUNCTIONAL-LINK NEURAL NETWORK CONTROLLER......Page 204
  4.2.1 Approximation by One-Layer Functional-Link NN......Page 205
  4.2.2 NN Controller and Error System Dynamics......Page 206
  4.2.3 Unsupervised Backpropagation Weight Tuning......Page 207
  4.2.4 Augmented Unsupervised Backpropagation Tuning- Removing the PE Condition......Page 212
  4.2.5 Functional-Link NN Controller Design and Simulation Example......Page 215
 4.3 TWO-LAYER NEURAL NETWORK CONTROLLER......Page 216
  4.3.1 NN Approximation and the Nonlinearity in the Parameters Problem......Page 219
  4.3.2 Controller Structure and Error System Dynamics......Page 221
  4.3.3 Weight Updates for Guaranteed Tracking Performance......Page 223
  4.4.1 Partitioned NN......Page 231
  4.4.3 Selection of a Basis Set for the Functional-Link NN......Page 234
  4.5.1 Passivity of the Tracking Error Dynamics......Page 237
  4.5.2 Passivity Properties of NN Controllers......Page 238
 4.6 CONCLUSIONS......Page 241
 4.7 REFERENCES......Page 242
 4.8 PROBLEMS......Page 244
5 Neural Network Robot Control: Applications and Extensions......Page 246
 5.1 FORCE CONTROL USING NEURAL NETWORKS......Page 247
  5.1.1 Force Constrained Motion and Error Dynamics......Page 248
  5.1.2 Neural Network Hybrid Position/Force Controller......Page 250
  5.1.3 Design Example for NN Hybrid Position/Force Controller......Page 257
  5.2.1 Flexible-Link Robot Arms......Page 258
  5.2.2 Robots with Actuators and Compliant Drive Train Coupling......Page 263
  5.2.3 Rigid-Link Electrically-Driven (RLED) Robot Arms......Page 269
 5.3 SINGULAR PERTURBATION DESIGN......Page 270
  5.3.1 Two-Time-Scale Controller Design......Page 271
  5.3.2 NN Controller for Flexible-Link Robot Using Singular Perturbations......Page 274
  5.4.1 Backstepping Design......Page 283
  5.4.2 NN Controller for Rigid-Link Electrically-Driven Robot Using Backstepping......Page 287
 5.5 CONCLUSIONS......Page 292
 5.6 REFERENCES......Page 295
 5.7 PROBLEMS......Page 297
6 Neural Network Control of Nonlinear Systems......Page 302
 6.1 SYSTEM AND TRACKING ERROR DYNAMICS......Page 303
  6.1.1 Tracking Controller and Error Dynamics......Page 304
 6.2 CASE OF KNOWN FUNCTION g(x)......Page 306
  6.2.1 Proposed NN Controller......Page 307
  6.2.2 NN Weight Tuning for Tracking Stability......Page 308
  6.2.3 Illustrative Simulation Example......Page 311
  6.3.1 Proposed NN Controller......Page 312
  6.3.2 NN Weight Tuning for Tracking Stability......Page 314
  6.3.3 Illustrative Simulation Examples......Page 321
 6.4 CONCLUSIONS......Page 326
 6.5 REFERENCES......Page 328
7 NN Control with Discrete-Time Tuning......Page 330
  7.1.1 Neural Network Approximation Property......Page 331
  7.1.3 Tracking Error Dynamics for a Class of Nonlinear Systems......Page 333
 7.2 ONE-LAYER NEURAL NETWORK CONTROLLER DESIGN......Page 335
  7.2.1 Structure of the One-layer NN Controller and Error System Dynamics......Page 336
  7.2.2 One-layer Neural Network Weight Updates......Page 337
  7.2.3 Projection Algorithm......Page 341
  7.2.5 One-layer Neural Network Weight Tuning Modification for Relaxation of Persistency of Excitation Condition......Page 346
 7.3 MULTILAYER NEURAL NETWORK CONTROLLER DESIGN......Page 352
  7.3.1 Structure of the NN Controller and Error System Dynamics......Page 355
  7.3.2 Multilayer Neural Network Weight Updates......Page 356
  7.3.3 Projection Algorithm......Page 363
  7.3.4 Multilayer Neural Network Weight Tuning Modification for Relaxation of Persistency of Excitation Condition......Page 365
  7.4.1 Passivity Properties of the Tracking Error System......Page 375
  7.4.2 Passivity Properties of One-layer Neural Networks and the Closed-Loop System......Page 377
  7.4.3 Passivity Properties of Multilayer Neural Networks......Page 378
 7.6 REFERENCES......Page 379
 7.7 PROBLEMS......Page 381
8 Discrete-Time Feedback Linearization by Neural Networks......Page 384
  8.1.1 Tracking Error Dynamics for a Class of Nonlinear Systems......Page 385
 8.2 NN CONTROLLER DESIGN FOR FEEDBACK LINEARIZATION......Page 387
  8.2.1 NN Approximation of Unknown Functions......Page 388
  8.2.2 Error System Dynamics......Page 389
  8.2.3 Well-Defined Control Problem......Page 391
 8.3 SINGLE-LAYER NN FOR FEEDBACK LINEARIZATION......Page 392
  8.3.1 Weight Updates Requiring Persistence of Excitation......Page 393
  8.3.2 Projection Algorithm......Page 400
  8.3.3 Weight Updates not Requiring Persistence of Excitation......Page 401
 8.4 MULTILAYER NEURAL NETWORKS FOR FEEDBACK LINEARIZATION......Page 408
  8.4.1 Weight Updates Requiring Persistence of Excitation......Page 409
  8.4.2 Weight Updates not Requiring Persistence of Excitation......Page 415
 8.5 PASSIVITY PROPERTIES OF THE NN......Page 427
  8.5.1 Passivity Properties of the Tracking Error System......Page 430
  8.5.2 Passivity Properties of One-layer Neural Network Controllers......Page 431
  8.5.3 Passivity Properties of Multilayer Neural Network Controllers......Page 432
 8.7 REFERENCES......Page 434
 8.8 PROBLEMS......Page 436
9 State Estimation Using Discrete-Time Neural Networks......Page 438
 9.2 IDENTIFIER DYNAMICS FOR MIMO SYSTEMS......Page 440
  9.3.1 Structure of the NN Controller and Error System Dynamics......Page 443
  9.3.2 Three-Layer Neural Network Weight Updates......Page 445
 9.4 PASSIVITY PROPERTIES OF THE NN......Page 450
 9.5 SIMULATION RESULTS......Page 452
 9.7 REFERENCES......Page 453
 9.8 PROBLEMS......Page 455