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Cover image for Neural network control of nonlinear discrete-time systems
Title:
Neural network control of nonlinear discrete-time systems
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Publication Information:
Boca Raton : CRC/Taylor & Francis , 2006
Physical Description:
1, 602 p. : ill. ; 24 cm.
ISBN:
9780824726775

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30000010117125 TJ213 S27 2006 Open Access Book Book
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Summary

Summary

Intelligent systems are a hallmark of modern feedback control systems. But as these systems mature, we have come to expect higher levels of performance in speed and accuracy in the face of severe nonlinearities, disturbances, unforeseen dynamics, and unstructured uncertainties. Artificial neural networks offer a combination of adaptability, parallel processing, and learning capabilities that outperform other intelligent control methods in more complex systems.

Borrowing from Biology
Examining neurocontroller design in discrete-time for the first time, Neural Network Control of Nonlinear Discrete-Time Systems presents powerful modern control techniques based on the parallelism and adaptive capabilities of biological nervous systems. At every step, the author derives rigorous stability proofs and presents simulation examples to demonstrate the concepts.

Progressive Development
After an introduction to neural networks, dynamical systems, control of nonlinear systems, and feedback linearization, the book builds systematically from actuator nonlinearities and strict feedback in nonlinear systems to nonstrict feedback, system identification, model reference adaptive control, and novel optimal control using the Hamilton-Jacobi-Bellman formulation. The author concludes by developing a framework for implementing intelligent control in actual industrial systems using embedded hardware.

Neural Network Control of Nonlinear Discrete-Time Systems fosters an understanding of neural network controllers and explains how to build them using detailed derivations, stability analysis, and computer simulations.


Table of Contents

Chapter 1 Background on Neural Networksp. 1
1.1 NN Topologies and Recallp. 2
1.1.1 Neuron Mathematical Modelp. 3
1.1.2 Multilayer Perceptronp. 8
1.1.3 Linear-in-the-Parameter NNp. 12
1.1.3.1 Gaussian or Radial Basis Function Networksp. 12
1.1.3.2 Cerebellar Model Articulation Controller Networksp. 13
1.1.4 Dynamic NNp. 15
1.1.4.1 Hopfield Networkp. 15
1.1.4.2 Generalized Recurrent NNp. 19
1.2 Properties of NNp. 24
1.2.1 Classification and Associationp. 25
1.2.1.1 Classificationp. 25
1.2.1.2 Associationp. 28
1.2.2 Function Approximationp. 31
1.3 NN Weight Selection and Trainingp. 35
1.3.1 Weight Computationp. 36
1.3.2 Training the One-Layer NN-Gradient Descentp. 38
1.3.2.1 Gradient Descent Tuningp. 39
1.3.2.2 Epoch vs. Batch Updatingp. 42
1.3.3 Training the Multilayer NN-Backpropagation Tuningp. 47
1.3.3.1 Backgroundp. 49
1.3.3.2 Derivation of the Backpropagation Algorithmp. 51
1.3.3.3 Improvements on Gradient Descentp. 63
1.3.4 Hebbian Tuningp. 67
1.4 NN Learning and Control Architecturesp. 69
1.4.1 Unsupervised and Reinforcement Learningp. 69
1.4.2 Comparison of the Two NN Control Architecturesp. 70
Referencesp. 71
Problemsp. 73
Chapter 2 Background and Discrete-Time Adaptive Controlp. 75
2.1 Dynamical Systemsp. 75
2.1.1 Discrete-Time Systemsp. 75
2.1.2 Brunovsky Canonical Formp. 76
2.1.3 Linear Systemsp. 77
2.2 Mathematical Backgroundp. 79
2.2.1 Vector and Matrix Normsp. 79
2.2.2 Continuity and Function Normsp. 82
2.3 Properties of Dynamical Systemsp. 83
2.3.1 Stabilityp. 83
2.3.2 Passivityp. 86
2.3.3 Interconnections of Passive Systemsp. 87
2.4 Nonlinear Stability Analysis and Controls Designp. 88
2.4.1 Lyapunov Analysis for Autonomous Systemsp. 88
2.4.2 Controller Design Using Lyapunov Techniquesp. 92
2.4.3 Lyapunov Analysis for Nonautonomous Systemsp. 97
2.4.4 Extensions of Lyapunov Techniques and Bounded Stabilityp. 99
2.5 Robust Implicit STRp. 102
2.5.1 Backgroundp. 104
2.5.1.1 Adaptive Control Formulationp. 105
2.5.1.2 Stability of Dynamical Systemsp. 106
2.5.2 STR Designp. 111
2.5.2.1 Structure of the STR and Error System Dynamicsp. 111
2.5.2.2 STR Parameter Updatesp. 112
2.5.3 Projection Algorithmp. 116
2.5.4 Ideal Case: No Disturbances and No STR Reconstruction Errorsp. 117
2.5.5 Parameter-Tuning Modification for Relaxation of PE Conditionp. 119
2.5.6 Passivity Properties of the STRp. 123
2.5.7 Conclusionsp. 127
Referencesp. 127
Problemsp. 129
Appendix 2.Ap. 131
Chapter 3 Neural Network Control of Nonlinear Systems and Feedback Linearizationp. 139
3.1 NN Control with Discrete-Time Tuningp. 142
3.1.1 Dynamics of the mnth Order Multi-Input and Multi-Output Discrete-Time Nonlinear Systemp. 143
3.1.2 One-Layer NN Controller Designp. 145
3.1.2.1 NN Controller Designp. 146
3.1.2.2 Structure of the NN and Error System Dynamicsp. 147
3.1.2.3 Weight Updates of the NN for Guaranteed Tracking Performancep. 148
3.1.2.4 Projection Algorithmp. 155
3.1.2.5 Ideal Case: No Disturbances and No NN Reconstruction Errorsp. 156
3.1.2.6 Parameter Tuning Modification for Relaxation of PE Conditionp. 160
3.1.3 Multilayer NN Controller Designp. 167
3.1.3.1 Error Dynamics and NN Controller Structurep. 170
3.1.3.2 Multilayer NN Weight Updatesp. 172
3.1.3.3 Projection Algorithmp. 179
3.1.3.4 Multilayer NN Weight-Tuning Modification for Relaxation of PE Conditionp. 185
3.1.4 Passivity of the NNp. 191
3.1.4.1 Passivity Properties of the Tracking Error Systemp. 191
3.1.4.2 Passivity Properties of One-Layer NNp. 192
3.1.4.3 Passivity of the Closed-Loop Systemp. 195
3.1.4.4 Passivity of the Multilayer NNp. 196
3.2 Feedback Linearizationp. 197
3.2.1 Input-Output Feedback Linearization Controllersp. 197
3.2.1.1 Error Dynamicsp. 198
3.2.2 Controller Designp. 199
3.3 NN Feedback Linearizationp. 200
3.3.1 System Dynamics and Tracking Problemp. 201
3.3.2 NN Controller Design for Feedback Linearizationp. 204
3.3.2.1 NN Approximation of Unknown Functionsp. 204
3.3.2.2 Error System Dynamicsp. 206
3.3.2.3 Well-Defined Control Problemp. 209
3.3.2.4 Controller Designp. 210
3.3.3 One-Layer NN for Feedback Linearizationp. 211
3.3.3.1 Weight Updates Requiring PEp. 211
3.3.3.2 Projection Algorithmp. 222
3.3.3.3 Weight Updates not Requiring PEp. 223
3.4 Multilayer NN for Feedback Linearizationp. 233
3.4.1 Weight Updates Requiring PEp. 234
3.4.2 Weight Updates Not Requiring PEp. 236
3.5 Passivity Properties of the NNp. 254
3.5.1 Passivity Properties of the Tracking Error Systemp. 255
3.5.2 Passivity Properties of One-Layer NN Controllersp. 256
3.5.3 Passivity Properties of Multilayer NN Controllersp. 256
3.6 Conclusionsp. 259
Referencesp. 259
Problemsp. 262
Chapter 4 Neural Network Control of Uncertain Nonlinear Discrete-Time Systems with Actuator Nonlinearitiesp. 265
4.1 Background on Actuator Nonlinearitiesp. 266
4.1.1 Frictionp. 266
4.1.1.1 Static Friction Modelsp. 267
4.1.1.2 Dynamic Friction Modelsp. 268
4.1.2 Deadzonep. 269
4.1.3 Backlashp. 272
4.1.4 Saturationp. 273
4.2 Reinforcement NN Learning Control with Saturationp. 274
4.2.1 Nonlinear System Descriptionp. 276
4.2.2 Controller Design Based on the Filtered Tracking Errorp. 277
4.2.3 One-Layer NN Controller Designp. 279
4.2.3.1 The Strategic Utility Functionp. 279
4.2.3.2 Critic NNp. 280
4.2.3.3 Action NNp. 281
4.2.4 NN Controller without Saturation Nonlinearityp. 283
4.2.5 Adaptive NN Controller Design with Saturation Nonlinearityp. 287
4.2.5.1 Auxiliary System Designp. 287
4.2.5.2 Adaptive NN Controller Structure with Saturationp. 288
4.2.5.3 Closed-Loop System Stability Analysisp. 288
4.2.6 Comparison of Tracking Error and Reinforcement Learning-Based Controls Designp. 296
4.3 Uncertain Nonlinear System with Unknown Deadzone and Saturation Nonlinearitiesp. 297
4.3.1 Nonlinear System Description and Error Dynamicsp. 300
4.3.2 Deadzone Compensation with Magnitude Constraintsp. 300
4.3.2.1 Deadzone Nonlinearityp. 300
4.3.2.2 Compensation of Deadzone Nonlinearityp. 301
4.3.2.3 Saturation Nonlinearitiesp. 303
4.3.3 Reinforcement Learning NN Controller Designp. 304
4.3.3.1 Error Dynamicsp. 304
4.3.3.2 Critic NN Designp. 305
4.3.3.3 Main Resultp. 306
4.4 Adaptive NN Control of Nonlinear System with Unknown Backlashp. 309
4.4.1 Nonlinear System Descriptionp. 310
4.4.2 Controller Design Using Filtered Tracking Error without Backlash Nonlinearityp. 311
4.4.3 Backlash Compensation Using Dynamic Inversionp. 312
4.5 Conclusionsp. 319
Referencesp. 320
Problemsp. 323
Appendix 4.Ap. 325
Appendix 4.Bp. 329
Appendix 4.Cp. 330
Appendix 4.Dp. 338
Chapter 5 Output Feedback Control of Strict Feedback Nonlinear MIMO Discrete-Time Systemsp. 343
5.1 Class of Nonlinear Discrete-Time Systemsp. 345
5.2 Output Feedback Controller Designp. 345
5.2.1 Observer Designp. 346
5.2.2 NN Controller Designp. 347
5.2.2.1 Auxiliary Controller Designp. 348
5.2.2.2 Controller Design with Magnitude Constraintsp. 349
5.3 Weight Updates for Guaranteed Performancep. 350
5.3.1 Weights Updating Rule for the Observer NNp. 350
5.3.2 Strategic Utility Functionp. 351
5.3.3 Critic NN Designp. 351
5.3.4 Weight-Updating Rule for the Action NNp. 353
5.4 Conclusionsp. 361
Referencesp. 362
Problemsp. 363
Appendix 5.Ap. 364
Appendix 5.Bp. 366
Chapter 6 Neural Network Control of Nonstrict Feedback Nonlinear Systemsp. 371
6.1 Introductionp. 371
6.1.1 Nonlinear Discrete-Time Systems in Nonstrict Feedback Formp. 371
6.1.2 Backstepping Designp. 373
6.2 Adaptive NN Control Design Using State Measurementsp. 374
6.2.1 Tracking Error-Based Adaptive NN Controller Designp. 375
6.2.1.1 Adaptive NN Backstepping Controller Designp. 375
6.2.1.2 Weight Updatesp. 378
6.2.2 Adaptive Critic-Based NN Controller Designp. 381
6.2.2.1 Critic NN Designp. 382
6.2.2.2 Weight-Tuning Algorithmsp. 383
6.3 Output Feedback NN Controller Designp. 392
6.3.1 NN Observer Designp. 394
6.3.2 Adaptive NN Controller Designp. 396
6.3.3 Weight Updates for the Output Feedback Controllerp. 400
6.4 Conclusionsp. 406
Referencesp. 407
Problemsp. 409
Appendix 6.Ap. 411
Appendix 6.Bp. 419
Chapter 7 System Identification Using Discrete-Time Neural Networksp. 423
7.1 Identification of Nonlinear Dynamical Systemsp. 425
7.2 Identifier Dynamics for MIMO Systemsp. 426
7.3 NN Identifier Designp. 429
7.3.1 Structure of the NN Identifier and Error System Dynamicsp. 430
7.3.2 Multilayer NN Weight Updatesp. 432
7.4 Passivity Properties of the NNp. 439
7.5 Conclusionsp. 443
Referencesp. 444
Problemsp. 444
Chapter 8 Discrete-Time Model Reference Adaptive Controlp. 447
8.1 Dynamics of an mnth-Order Multi-Input and Multi-Output Systemp. 448
8.2 NN Controller Designp. 451
8.2.1 NN Controller Structure and Error System Dynamicsp. 451
8.2.2 Weight Updates for Guaranteed Tracking Performancep. 454
8.3 Projection Algorithmp. 460
8.4 Conclusionsp. 468
Referencesp. 469
Problemsp. 470
Chapter 9 Neural Network Control in Discrete-Time Using Hamilton-Jacobi-Bellman Formulationp. 473
9.1 Optimal Control and Generalized HJB Equation in Discrete-Timep. 475
9.2 NN Least-Squares Approachp. 486
9.3 Numerical Examplesp. 490
9.4 Conclusionsp. 508
Referencesp. 508
Problemsp. 509
Chapter 10 Neural Network Output Feedback Controller Design and Embedded Hardware Implementationp. 511
10.1 Embedded Hardware-PC Real-Time Digital Control Systemp. 512
10.1.1 Hardware Descriptionp. 512
10.1.2 Software Descriptionp. 514
10.2 SI Engine Test Bedp. 514
10.2.1 Engine-PC Interface Hardware Operationp. 516
10.2.2 PC Operationp. 518
10.2.3 Timing Specifications for Controllerp. 520
10.2.4 Software Implementationp. 521
10.3 Lean Engine Controller Design and Implementationp. 523
10.3.1 Engine Dynamicsp. 526
10.3.2 NN Observer Designp. 528
10.3.3 Adaptive NN Output Feedback Controller Designp. 530
10.3.3.1 Adaptive NN Backstepping Designp. 531
10.3.3.2 Weight Updates for Guaranteed Performancep. 535
10.3.4 Simulation of NN Controller C Implementationp. 537
10.3.5 Experimental Resultsp. 539
10.4 EGR Engine Controller Design and Implementationp. 547
10.4.1 Engine Dynamics with EGRp. 549
10.4.2 NN Observer Designp. 551
10.4.3 Adaptive Output Feedback EGR Controller Designp. 553
10.4.3.1 Error Dynamicsp. 554
10.4.3.2 Weight Updates for Guaranteed Performancep. 557
10.4.4 Numerical Simulationp. 559
10.5 Conclusionsp. 563
Referencesp. 564
Problemsp. 565
Appendix 10.Ap. 566
Appendix 10.Bp. 570
Indexp. 595
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