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Recent Developments in Automatic Control Systems RIVER PUBLISHERS SERIES IN AUTOMATION, CONTROL AND ROBOTICS SeriesEditors: ISHWARK.SETHI OaklandUniversity,USA TAREKSOBH UniversityofBridgeport,USA FENGQIAO ShenyangJianZhuUniversity,China The“RiverPublishersSeriesinAutomation,ControlandRobotics”isaseries ofcomprehensiveacademicandprofessionalbookswhichfocusonthetheory and applications of automation, control and robotics. The series focuses on topics ranging from the theory and use of control systems, automation engineering,roboticsandintelligentmachines. Books published in the series include research monographs, edited volumes, handbooks and textbooks. The books provide professionals, researchers, educators, and advanced students in the field with an invaluable insightintothelatestresearchanddevelopments. Topicscoveredintheseriesinclude,butarebynomeansrestrictedtothe following: • RobotsandIntelligentMachines • Robotics • ControlSystems • ControlTheory • AutomationEngineering Foralistofotherbooksinthisseries,visitwww.riverpublishers.com A Comprehensive Study of the Recent Developments in Automatic Control Systems Editors Yuriy P. Kondratenko PetroMohylaBlackSeaNationalUniversityoftheMinistryofEducation andScienceofUkraine,Ukraine Vsevolod M. Kuntsevich SpaceResearchInstituteoftheNationalAcademyofSciencesofUkraine andStateSpaceAgencyofUkraine,Ukraine Arkadii A. Chikrii GlushkovInstituteofCyberneticsoftheNationalAcademyofSciencesof Ukraine,Ukraine Vyacheslav F. Gubarev SpaceResearchInstituteoftheNationalAcademyofSciencesofUkraine andStateSpaceAgencyofUkraine,Ukraine River Publishers Published2023byRiverPublishers RiverPublishers Alsbjergvej10,9260Gistrup,Denmark www.riverpublishers.com DistributedexclusivelybyRoutledge 605ThirdAvenue,NewYork,NY10017,USA 4ParkSquare,MiltonPark,Abingdon,OxonOX144RN Recent Developments in Automatic Control Systems/by Yuriy P. Kon- dratenko,VsevolodM.Kuntsevich,ArkadiiA.Chikrii. ©2023RiverPublishers.Allrightsreserved.Nopartofthispublicationmay bereproduced,storedinaretrievalsystems,ortransmittedinanyformorby anymeans,mechanical,photocopying,recordingorotherwise,withoutprior writtenpermissionofthepublishers. RoutledgeisanimprintoftheTaylor&FrancisGroup,aninforma business ISBN978-87-7022-674-5(print) ISBN978-10-0079-560-8(online) ISBN978-10-0333-922-9(ebookmaster) While every effort is made to provide dependable information, the publisher, authors, and editors cannot be held responsible for any errors oromissions. Contents Preface xiii ListofFigures xxi ListofTables xxix ListofContributors xxxi ListofNotationsandAbbreviations xxxv PartIAdvancesinTheoreticalResearchofControlSystems 1 1 ControlofMovingObjectGroupsina ConflictSituation 3 A.Chikrii 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Functionω(n,ν),EncirclementbyPshenihnyi,Scheme oftheMethodofResolvingFunctions . . . . . . . . . . . . 4 1.3 GroupPursuitofaMovingObject . . . . . . . . . . . . . . 9 1.4 Non-fixedTimeofGameTermination . . . . . . . . . . . . 14 1.5 TheGroupPursuit.LinearStateConstraints . . . . . . . . . 17 1.6 PrincipleofShortestBrokenLineinSuccessivePursuit . . . 22 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2 Applications of Variational Analysis to Controlled Sweeping Processes 31 BorisS.Mordukhovich 2.1 IntroductionandDiscussions . . . . . . . . . . . . . . . . . 32 2.2 GeneralizedDifferentiationofVariationalAnalysis . . . . . 36 2.3 DynamicOptimizationviaControlledMovingSets . . . . . 39 2.4 SweepingProcesseswithControlledDynamics . . . . . . . 48 v vi Contents 2.5 SomeApplications . . . . . . . . . . . . . . . . . . . . . . 51 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 56 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3 Robust and Robustly-Adaptive Control of Some Noninvertible MemorylessSystems 61 L.ZhiteckiiandK.Solovchuk 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2 ProblemStatement . . . . . . . . . . . . . . . . . . . . . . 63 3.3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4 RobustNonadaptiveControl . . . . . . . . . . . . . . . . . 69 3.5 Robustly-AdaptiveControlofSquareSystems(Case1) . . . 76 3.6 Robustly-AdaptiveControlofSquareSystems(Case2) . . . 84 3.7 Robustly-AdaptiveControlofNonsquareSystems . . . . . . 86 3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 91 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4 NonlinearIntegralInequalitiesandDifferentialGames ofAvoidingEncounter 97 L.P.Yugay 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.1.1 OntheFirstIntegralInequalities . . . . . . . . . . . 97 4.1.2 DevelopmentoftheTheoryofIntegralInequalities (BriefSurvey). . . . . . . . . . . . . . . . . . . . . 98 4.2 InvestigationofNonlinearHölderTypeIntegral Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.2.1 MainResults . . . . . . . . . . . . . . . . . . . . . 100 4.2.2 ApplicationsofIntegralInequalitiesinDifferential GamesofAvoidinganEncounter . . . . . . . . . . 104 4.2.3 ComparisonofResults . . . . . . . . . . . . . . . . 105 4.2.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . 106 4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 107 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5 PrincipleofTimeDilationinGameProblemsofDynamics 113 G.Ts.Chikrii 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Contents vii 5.2 StatementoftheGameProblem.ClassicandModified Pontryagin’sCondition . . . . . . . . . . . . . . . . . . . . 116 5.3 MethodScheme . . . . . . . . . . . . . . . . . . . . . . . . 118 5.4 MainStatement . . . . . . . . . . . . . . . . . . . . . . . . 120 5.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 126 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6 Method of Upper and Lower Resolving Functions for Pursuit Differential-differenceGameswithPureDelay 131 L.V.Baranovska 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.2 StatementoftheProblem . . . . . . . . . . . . . . . . . . . 132 6.3 SchemeoftheMethod . . . . . . . . . . . . . . . . . . . . 134 6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 138 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 7 AdaptiveMethodfortheVariationalInequalityProblemOver theSetofSolutionsofthe EquilibriumProblem 145 Y.Vedel,S.Denisov,andV.Semenov 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 146 7.2 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . 147 7.3 Tikhonov–BrowderApproximation . . . . . . . . . . . . . . 148 7.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7.5 ProofofAlgorithmConvergence . . . . . . . . . . . . . . . 152 7.6 AlgorithmforTwo-LevelVariationalInequalities . . . . . . 158 7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Acknowlegdments. . . . . . . . . . . . . . . . . . . . . . . 160 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 PartIIAdvancesinControlSystemsApplication 165 8 IdentificationofComplexSystemsintheClassofLinear RegressionModels 167 V.Gubarev,S.Melnychuk,andN.Salnikov 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.2 ActiveExperimentsandInformativeData . . . . . . . . . . 169 8.3 MethodofIdentification . . . . . . . . . . . . . . . . . . . 173 8.3.1 ModelOrderSelection . . . . . . . . . . . . . . . . 173 viii Contents 8.3.2 SVDParametricIdentification . . . . . . . . . . . . 176 8.3.3 TotalModelReconstruction . . . . . . . . . . . . . 176 8.3.4 QuasioptimalModelDimensions. . . . . . . . . . . 177 8.4 SimulationResults . . . . . . . . . . . . . . . . . . . . . . 178 8.4.1 Algorithmofidentification . . . . . . . . . . . . . . 179 8.4.2 Excitationofsystemmodes . . . . . . . . . . . . . 181 8.4.3 EffectofUsingtheSignalPartofMatrices . . . . . 186 8.4.4 EffectofDiscardingDataClosetoNoise . . . . . . 187 8.4.5 TheBestSystemsforIdentification . . . . . . . . . 188 8.4.6 ModelOrderDetermination . . . . . . . . . . . . . 188 8.4.7 MaximumDimensionofIdentifiableModel . . . . . 192 8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 193 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 9 FuzzySystemsDesign:OptimalSelectionofLinguisticTerms Number 197 OleksiyKozlov,YuriyKondratenko,OleksandrSkakodub, andZbigniewGomolka 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 198 9.2 RelatedWorksandProblemStatement . . . . . . . . . . . . 199 9.3 InformationTechnologyforFuzzySystemsDesign andStructuralOptimizationwithOptimalSelection ofLinguisticTermsNumber . . . . . . . . . . . . . . . . . 204 9.4 Design and Structural Optimization of the Fuzzy Control SystemfortheQuadrotorUnmannedAerialVehicle . . . . . 214 9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 228 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 10 AnalysisoftheDynamicsandControllabilityofanAutonomous MobileRobotwithaManipulator 241 AshhepkovaNatalja,ZbrutskyAlexander, andKoshevoyNicolay 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 242 10.2 Results of Study of Dynamics and Control of Autonomous MobileRobots . . . . . . . . . . . . . . . . . . . . . . . . 244 10.2.1 ProblemStatement . . . . . . . . . . . . . . . . . . 244 10.2.2 DesignofanAutonomousMobileRobot withaManipulator . . . . . . . . . . . . . . . . . . 246 Contents ix 10.2.3 DynamicsAnalysis . . . . . . . . . . . . . . . . . . 247 10.2.4 AnalysisofAMRwithMControllability . . . . . . 253 10.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 257 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 11 SafeNavigationofanAutonomousRobotinDynamic andUnknownEnvironments 261 YuriyP.Kondratenko,ArashRoshanineshat, andDanSimon 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.2 RelatedWorks . . . . . . . . . . . . . . . . . . . . . . . . . 263 11.3 ProblemStatement . . . . . . . . . . . . . . . . . . . . . . 267 11.4 FuzzybasedPathPlanning . . . . . . . . . . . . . . . . . . 269 11.5 AdjustingSpeed . . . . . . . . . . . . . . . . . . . . . . . . 275 11.6 ExperimentsandEvaluations . . . . . . . . . . . . . . . . . 275 11.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 278 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 12 AlgorithmicProceduresSynthesisofRobust-OptimalControl forMovingObjects 289 V.L.Timchenko,andD.O.Lebedev 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 290 12.2 ProblemReview . . . . . . . . . . . . . . . . . . . . . . . . 294 12.3 OptimalSynthesis . . . . . . . . . . . . . . . . . . . . . . . 296 12.3.1 OptimalTrajectoryPlanning . . . . . . . . . . . . . 297 12.3.2 DeterminingSwitchingMomentsofControl FunctionsintheFeedbackLoops. . . . . . . . . . . 302 12.3.3 SynthesizingOptimalControlFunctions intheCorrespondingFeedbackLoops . . . . . . . . 302 12.4 RobustCorrection . . . . . . . . . . . . . . . . . . . . . . . 305 12.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 309 12.5.1 SeaVesselManeuvering . . . . . . . . . . . . . . . 309 12.5.2 QuadrotorUAVStabilization . . . . . . . . . . . . . 311 12.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 317 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 318