Table Of ContentAdvanced Control Systems:
Theory and Applications
River Publishers Series in Automation, Control and Robotics
SeriesEditors:
IshwarK.Sethi TarekSobh
OaklandUniversity UniversityofBridgeport
USA USA
FengQiao
ShenyangJianZhuUniversity
China
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Advanced Control Systems:
Theory and Applications
Editors
Yuriy P. Kondratenko
Vsevolod M. Kuntsevich
Arkadii A. Chikrii
Vyacheslav F. Gubarev
River Publishers
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Contents
Preface xiii
ListofContributors xix
ListofFigures xxiii
ListofTables xxix
ListofAbbreviations xxxi
I AdvancesinTheoreticalResearchonAutomaticControl 1
1 OnDescriptorControlImpulsiveDelaySystemsthatArisein
Lumped-DistributedCircuits 3
A.Chikrii,A.RutkasandL.Vlasenko 3
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 ExampleofDescriptorControlSystem . . . . . . . . . . . . 5
1.3 Restrictions,Definitions,andStatesofSystem . . . . . . . . 8
1.4 ANonlinearCircuitwithTransmissionLinesinthePresence 13
1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 AnExtremalRoutingProblemwithConstraintsandComplicated
CostFunctions 21
A.A.Chentsov,A.G.Chentsov,andA.N.Sesekin 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 GeneralNotionsandDesignations . . . . . . . . . . . . . . 23
2.3 GeneralRoutingProblemandItsSpecificVariant . . . . . . 24
2.4 DynamicProgramming,1 . . . . . . . . . . . . . . . . . . . 29
2.5 DynamicProgramming,2 . . . . . . . . . . . . . . . . . . . 39
2.6 ComputationalExperiment . . . . . . . . . . . . . . . . . . 44
v
vi Contents
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.8 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . 49
3 Principle of Time Stretching for Motion Control in Condition
ofConflict 53
G.Ts.Chikrii 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 Equivalence of the Pursuit Game with Delay of Information
totheGame . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3 PrincipleofTimeStretchinginDynamicGamesofPursuit . 60
3.4 Integro-DifferentialGameofPursuit . . . . . . . . . . . . . 65
3.5 IllustrativeExampleoftheIntegro-DifferentialGameofPursuit 70
3.6 SoftMeetingofMathematicalPendulums . . . . . . . . . . 73
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4 Bio-Inspired Algorithms for Optimization of Fuzzy Control
Systems:ComparativeAnalysis 83
OleksiyKozlov,YuriyKondratenko 83
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 RelatedWorksandProblemStatement . . . . . . . . . . . . 86
4.3 Bio-inspired Algorithms of Synthesis and Optimization of
RuleBases . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.3.1 ACO Algorithm for Synthesis and Optimization of
RuleBasesfortheMamdani-TypeFACS . . . . . . 90
4.3.2 Genetic Algorithm for Synthesis and Optimization
ofRuleBasesfortheMamdani-TypeFACS . . . . . 96
4.3.3 AlgorithmofAutomaticRuleBaseSynthesisforthe
Mamdani-TypeFACSBasedonSequentialSearch . 101
4.4 DevelopmentoftheRuleBaseoftheFuzzyControlSystem 104
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5 InverseModelApproachtoDisturbanceRejectionProblem 129
L.Lyubchyk 129
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.2 DisturbanceRejectionviaInverseModelControl . . . . . . 134
5.2.1 InverseModelControlPrinciple . . . . . . . . . . . 134
5.2.2 InverseModelDesign . . . . . . . . . . . . . . . . 136
5.2.3 InverseModelBasedFeedforwardControl . . . . . 141
5.2.4 InverseModelBasedDisturbanceObserver . . . . . 143
Contents vii
5.2.5 DisturbanceDecouplingCompensatorDesign . . . . 144
5.3 SlidingModeInverseModelControl . . . . . . . . . . . . . 147
5.3.1 SlidingModeEquivalencePrinciple . . . . . . . . . 147
5.3.2 5.3.2.VariableStructureFeedforwardCompensator . 150
5.3.3 VariableStructureDisturbanceObserver. . . . . . . 151
5.4 DiscreteInverseModelControl . . . . . . . . . . . . . . . . 153
5.4.1 ProblemStatement . . . . . . . . . . . . . . . . . . 153
5.4.2 DiscreteDisturbanceObserver . . . . . . . . . . . . 154
5.4.3 DisturbanceObserverParameterization . . . . . . . 156
5.4.4 DisturbanceCompensatorStructuralSynthesis . . . 157
5.4.5 DisturbanceCompensatorParametricSynthesis . . . 159
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6 Invariant Relations in the Theory of Optimally Controlled
Systems 167
B.Kiforenko,S.Kiforenko 167
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2 The Problems of Price–Target Invariance in the Theory of
OptimalControl . . . . . . . . . . . . . . . . . . . . . . . . 170
6.3 The Problems of Using Singular Controls in Rocket Flight
Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.3.1 Power Consumption in Degeneracy of the Optimal
ControlofRocketThrustinAtmosphere. . . . . . . 173
6.3.2 Necessary Conditions for the Optimality of a
SingularControl . . . . . . . . . . . . . . . . . . . 174
6.3.3 The Problem of Calculating Optimal Trajectories
WithSingularArcs . . . . . . . . . . . . . . . . . . 176
6.4 AdditiontotheFeldbaumTheoremonNumberofSwitching 180
6.5 InvestigationoftheInvarianceintheModelingofFunctioning 182
6.5.1 StatementoftheAnokhinProblem . . . . . . . . . . 182
6.5.2 SolutionoftheAnokhinProblem . . . . . . . . . . 183
6.5.3 Features of Expediently Functioning Objects with
RedundantControl . . . . . . . . . . . . . . . . . . 185
6.5.4 StructureoftheControllingSystemofanExpediently
FunctioningObject . . . . . . . . . . . . . . . . . . 187
6.5.5 Hierarchy and Invariance of Expediently Controlled
System . . . . . . . . . . . . . . . . . . . . . . . . 188
6.6 InvestigationAnalysisofResults . . . . . . . . . . . . . . . 189
viii Contents
6.6.1 Mathematical Modeling – A Tool for Research of
ComplexSystems. . . . . . . . . . . . . . . . . . . 189
6.6.2 OptimalityandEvolutionSelection . . . . . . . . . 190
6.6.3 Hierarchy and Invariance of Expediently Controlled
System . . . . . . . . . . . . . . . . . . . . . . . . 191
6.7 OptimalControlTheoryasaToolforCognition . . . . . . . 192
6.8 IsTeleologyTheological?. . . . . . . . . . . . . . . . . . . 194
6.9 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . 195
7 RobustAdaptiveControlsforaClassofNonsquareMemoryless
Systems 203
L.Zhiteckii,K.Solovchuk 203
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 204
7.2 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . 205
7.3 BackgroundonPseudoinverseModel-BasedMethod . . . . 207
7.4 RobustAdaptivePseudoinverseModel-BasedControllersfor
SIMOsystems . . . . . . . . . . . . . . . . . . . . . . . . . 212
7.5 Robust Adaptive Pseudoinverse Model-Based Control of
MIMOSystem . . . . . . . . . . . . . . . . . . . . . . . . 221
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 224
II AdvancesinControlSystemsApplications 229
8 Advanced Identification of Impulse Processes in Cognitive
Maps 231
VyacheslavGubarev,VictorRomanenko,andYuriiMiliavskyi 231
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 232
8.2 ProblemStatement . . . . . . . . . . . . . . . . . . . . . . 234
8.3 CMIdentificationFeatures . . . . . . . . . . . . . . . . . . 235
8.4 SubspaceIdentificationwithRegularization . . . . . . . . . 237
8.4.1 IdentificationforGivenModelDimension . . . . . . 239
8.4.2 ModelDimensionDetermination . . . . . . . . . . 242
8.5 AdvancedSubspaceIdentification . . . . . . . . . . . . . . 245
8.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
8.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Contents ix
9 Strategy for Simulation Complex Hierarchical Systems Based
ontheMethodologiesofForesightandCognitiveModeling 257
N.D.Pankratova,G.V.GorelovaandV.A.Pankratov 257
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 258
9.2 TheoreticalFoundationofForesightandCognitiveModeling
Methodologies . . . . . . . . . . . . . . . . . . . . . . . . 259
9.2.1 ForesightMethodologyofComplexSystem . . . . . 259
9.2.2 Methodology of Cognitive Modeling of Complex
Systems . . . . . . . . . . . . . . . . . . . . . . . . 262
9.2.3 RelationshipoftheEducationSystemwiththeSocio-
EconomicEnvironment. . . . . . . . . . . . . . . . 271
9.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 285
9.4 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . 286
10 Special Cases in Determining the Spacecraft Position and
AttitudeUsingComputerVisionSystem 289
V.Gubarev,N.Salnikov,S.Melnychuk,V.Shevchenko,
L.Maksymyuk 289
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 290
10.2 PnPProblemStatement . . . . . . . . . . . . . . . . . . . . 292
10.3 PnPProblemUnderUncertainty . . . . . . . . . . . . . . . 293
10.4 RotationParameterization . . . . . . . . . . . . . . . . . . 295
10.5 SensitivityofImage . . . . . . . . . . . . . . . . . . . . . 296
10.6 EstimatinganIndistinguishableSet. . . . . . . . . . . . . . 300
10.7 DesignofExperiment . . . . . . . . . . . . . . . . . . . . 302
10.8 NumericalSimulations . . . . . . . . . . . . . . . . . . . . 304
10.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 312
11 On Determining the Spacecraft Orientation by Information
fromaSystemofStellarSensors 317
DmitriyV.Lebedev 317
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 317
11.2 SystemsofCoordinates:FormulationoftheProblem . . . . 319
11.3 CorrespondenceofThree-DimensionalandFour-Dimensional
ParametersofaGroupofThree-DimensionalRotations . . . 320
11.4 Algorithms for Determining the Orientation Parameters of
theSpacecraft . . . . . . . . . . . . . . . . . . . . . . . . . 322
11.5 Accuracy Analysis of Determining the Parameters of the SC
Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . 324
