Radial Basis Function (RBF) Neural Network Control for Mechanical Systems: Design, Analysis and Matlab Simulation

373 Pages·2013·4.237 MB·English

by  Jinkun Liu (auth.)

Radial Basis Function (RBF) Neural Network
Control for Mechanical Systems

Jinkun Liu
Radial Basis Function (RBF)
Neural Network Control
for Mechanical Systems
Design, Analysis and Matlab Simulation
With 170 figures
JinkunLiu
DepartmentofIntelligentSystem
andControlEngineering
SchoolofAutomationScience
andElectricalEngineering
BeihangUniversity
Beijing,China,People’sRepublic
TUP ISBN 978-7-302-30255-1
ISBN978-3-642-34815-0 ISBN978-3-642-34816-7(eBook)
DOI10.1007/978-3-642-34816-7
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012955859
#TsinghuaUniversityPress,BeijingandSpringer-VerlagBerlinHeidelberg2013
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Preface
Recentyearshaveseenarapiddevelopmentofneuralnetworkcontroltechniques
andtheirsuccessfulapplications.Numeroustheoreticalstudiesandactualindustrial
implementationsdemonstratethatartificialneuralnetworkisagoodcandidatefor
functionapproximationandcontrolsystemdesigninsolvingthecontrolproblems
of complex nonlinear systems in the presence of different kinds of uncertainties.
Many control approaches/methods, reporting inventions and control applications
withinthefieldsofadaptivecontrol,neuralcontrol,andfuzzysystems,havebeen
publishedinvariousbooks,journals,andconferenceproceedings.Inspiteofthese
remarkable advances in neural control field, due to the complexity of nonlinear
systems, the present research on adaptive neural control is still focused on the
developmentoffundamentalmethodologies.
The advantage of neural networks is that a suitable number of neural network
functions can model any (sufficiently smooth) continuous nonlinear function in
acompactset,andthemodelingerrorisbecomingsmallerwithanincreaseofneural
networkfunctions.Itisevenpossibletomodeldiscontinuousnonlinearitiesassuming
therightchoiceofdiscontinuousneuralnetworkfunctions.Thus,anadaptiveneural
network approach is most suitable in an environment where system dynamics are
significantlychanging,highlynonlinear,andinprinciplenotcompletelyknown.
Thisbookismotivatedbytheneedforsystematicdesignapproachesforstable
adaptive control system design using neural network approximation-based
techniques. The main objectives of the book are to introduce the concrete design
method and Matlab simulation of stable adaptive RBF (Radial Basis Function)
neuralcontrolstrategies.
Itisourgoaltoaccomplishtheseobjectives:
• Offer a catalog of implementable neural network control design methods for
engineeringapplications.
• Provide advanced neural network controller design methods and their stability
analysismethods.
• Foreachneuralnetworkcontrolalgorithm,weofferitssimulationexampleand
Matlabprogram.
v
vi Preface
Thisbookprovidesthereaderwithathoroughgroundingintheneuralnetwork
control system design. Typical neural network controllers’ designs are verified
using Matlab simulation. In this book, concrete case studies, which present the
results of neural network controller implementations, are used to illustrate the
successfulapplicationofthetheory.
The book is structured as follows. The book starts with a brief introduction
of adaptive control and neural network control in Chap. 1, RBF neural network
algorithmanddesignremarksaregiveninChap.2,RBFneuralnetworkcontroller
design based on gradient descent algorithm is introduced in Chap. 3, since only
local optimization can be guaranteed by using the gradient descent method, and
several adaptive RBF neural network controller designs are given based on
Lyapunov analysis from Chaps. 4, 5, 6, 7 and 8, which include simple adaptive
RBF neural network controller, neural network sliding mode controller, adaptive
RBF controller based on global approximation, adaptive robust RBF controller
based on local approximation, and backstepping adaptive controller with RBF.
In Chap. 9, digital RBF neural network controller design is given. Two kinds of
discrete neural network controllers are introduced in Chap. 10. At last, a neural
networkadaptiveobserverisrecommendedandaspeedlessslidingmodecontroller
designisgiveninChap.11.
IwouldliketothankProf.S.S.Geforhisfruitfulsuggestions.Iwishtothank
myfamilyfortheirsupportandencouragement.
In this book, all the control algorithms and their programs are described sepa-
ratelyandclassifiedbythechaptername,whichcanberunsuccessfullyinMatlab
7.5.0.342versionorinothermoreadvancedversions.Inaddition,alltheprograms
can be downloaded via http://ljk.buaa.edu.cn/. If you have questions about
algorithmsandsimulationprograms,[email protected].
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 NeuralNetworkControl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 WhyNeuralNetworkControl?. . . . . . . . . . . . . . . . . . . . 1
1.1.2 ReviewofNeuralNetworkControl. . . . . . . . . . . . . . . . 2
1.1.3 ReviewofRBFAdaptiveControl. . . . . . . . . . . . . . . . . . 3
1.2 ReviewofRBFNeuralNetwork. . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 RBFAdaptiveControlforRobotManipulators. . . . . . . . . . . . . 4
1.4 SFunctionDesignforControlSystem. . . . . . . . . . . . . . . . . . . . 5
1.4.1 SFunctionIntroduction. . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.2 BasicParametersinSFunction. . . . . . . . . . . . . . . . . . . 5
1.4.3 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 AnExampleofaSimpleAdaptiveControlSystem. . . . . . . . . . . 7
1.5.1 SystemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5.2 AdaptiveControlLawDesign. . . . . . . . . . . . . . . . . . . . 7
1.5.3 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 RBFNeuralNetworkDesignandSimulation. . . . . . . . . . . . . . . . . 19
2.1 RBFNeuralNetworkDesignandSimulation. . . . . . . . . . . . . . . 19
2.1.1 RBFAlgorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.2 RBFDesignExamplewithMatlabSimulation. . . . . . . . 20
2.2 RBFNeuralNetworkApproximationBasedonGradient
DescentMethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 RBFNeuralNetworkApproximation. . . . . . . . . . . . . . . 22
2.2.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 EffectofGaussianFunctionParametersonRBF
Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 EffectofHiddenNetsNumberonRBFApproximation. . . . . . . 28
vii
viii Contents
2.5 RBFNeuralNetworkTrainingforSystemModeling. . . . . . . . . 33
2.5.1 RBFNeuralNetworkTraining. . . . . . . . . . . . . . . . . . . . 33
2.5.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 RBFNeuralNetworkApproximation. . . . . .. . . . . . .. . . . . . .. 36
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3 RBFNeuralNetworkControlBasedonGradient
DescentAlgorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 SupervisoryControlBasedonRBFNeuralNetwork.. . . .. . . .. 55
3.1.1 RBFSupervisoryControl. . . . . . . . . . . . . . . . . . . . . . . . 55
3.1.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 RBFNN-BasedModelReferenceAdaptiveControl. . . . . . . . . . 58
3.2.1 ControllerDesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 RBFSelf-AdjustControl.. . . . . . . . .. . . . . . . . .. . . . . . . . .. . 61
3.3.1 SystemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3.2 RBFControllerDesign. . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3.3 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4 AdaptiveRBFNeuralNetworkControl. . . . . . . . . . . . . . . . . . . . . 71
4.1 AdaptiveControlBasedonNeuralApproximation. . . . . . . . . . . 71
4.1.1 ProblemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1.2 AdaptiveRBFControllerDesign. . . . . . . . . . . . . . . . . . 72
4.1.3 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 AdaptiveControlBasedonNeuralApproximation
withUnknownParameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.1 ProblemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.2 AdaptiveControllerDesign. . . . . . . . . . . . . . . . . . . . . . 79
4.2.3 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3 ADirectMethodforRobustAdaptiveControlbyRBF. . . . . . . . 83
4.3.1 SystemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.2 DesiredFeedbackControlandFunction
Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.3 ControllerDesignandPerformanceAnalysis. . . . . . . . . 87
4.3.4 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5 NeuralNetworkSlidingModeControl. . . . . . . . . . . . . . . . . . . . . . 113
5.1 TypicalSlidingModeControllerDesign. . . . . . . . . . . . . . . . . . 114
5.2 SlidingModeControlBasedonRBFforSecond-Order
SISONonlinearSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2.1 ProblemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Contents ix
5.2.2 SlidingModeControlBasedonRBF
forUnknownfð(cid:2)Þ. . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 117
5.2.3 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.3 SlidingModeControlBasedonRBFforUnknownf((cid:2))
andg((cid:2)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.3.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6 AdaptiveRBFControlBasedonGlobalApproximation. . . . . . . . 133
6.1 AdaptiveControlwithRBFNeuralNetworkCompensation
forRoboticManipulators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.1.1 ProblemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.1.2 RBFApproximation. . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.1.3 RBFControllerandAdaptiveLawDesign
andAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.1.4 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.2 RBFNeuralRobotControllerDesignwithSlidingMode
RobustTerm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.2.1 ProblemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.2.2 RBFApproximation. . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2.3 ControlLawDesignandStabilityAnalysis. . . . . . . . . . . 147
6.2.4 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.3 RobustControlBasedonRBFNeuralNetworkwithHJI. . . . . . 153
6.3.1 Foundation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.3.2 ControllerDesignandAnalysis. . . . . . . . . . . . . . . . . . . 153
6.3.3 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
7 AdaptiveRobustRBFControlBasedonLocalApproximation. . . 193
7.1 RobustControlBasedonNominalModel
forRoboticManipulators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
7.1.1 ProblemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . 193
7.1.2 ControllerDesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
7.1.3 StabilityAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
7.1.4 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 196
7.2 AdaptiveRBFControlBasedonLocalModelApproximation
forRoboticManipulators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.2.1 ProblemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.2.2 ControllerDesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
7.2.3 StabilityAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
7.2.4 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 203
x Contents
7.3 AdaptiveNeuralNetworkControlofRobotManipulators
inTaskSpace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
7.3.1 CoordinationTransformationfromTaskSpace
toJointSpace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.3.2 NeuralNetworkModelingofRobotManipulators. . . . . . 208
7.3.3 ControllerDesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
7.3.4 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
8 BacksteppingControlwithRBF. . . . . . . . . . . . . . . . . . . . . . . . . . . 251
8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
8.2 BacksteppingControlforInvertedPendulum. . . . . . . . . . . . . . . 252
8.2.1 SystemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
8.2.2 ControllerDesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
8.2.3 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 254
8.3 BacksteppingControlBasedonRBFforInvertedPendulum. . . . 255
8.3.1 SystemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
8.3.2 BacksteppingControllerDesign. . . . . . . . . . . . . . . . . . . 256
8.3.3 AdaptiveLawDesign. . . . . . . . . . . . . . . . . . . . . . . . . . 257
8.3.4 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 259
8.4 BacksteppingControlforSingle-LinkFlexibleJointRobot. . . . . 260
8.4.1 SystemDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
8.4.2 BacksteppingControllerDesign. . . . . . . . . . . . . . . . . . . 262
8.5 AdaptiveBacksteppingControlwithRBFforSingle-Link
FlexibleJointRobot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
8.5.1 BacksteppingControllerDesignwithFunction
Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 265
8.5.2 BacksteppingControllerDesignwithRBF
Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
8.5.3 SimulationExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . 272
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
9 DigitalRBFNeuralNetworkControl. . . . . . . . . . . . . . . . . . . . . . . 293
9.1 AdaptiveRunge–Kutta–MersonMethod. . . . . . . . . . . . . . . . . . 293
9.1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
9.1.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 295
9.2 DigitalAdaptiveControlforSISOSystem. . . . . . . . . . . . . . . . . 295
9.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
9.2.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 297
9.3 DigitalAdaptiveRBFControlforTwo-LinkManipulators. . . . . 298
9.3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
9.3.2 SimulationExample. . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309