Table Of ContentDongyu Li
Shuzhi Sam Ge
Tong Heng Lee
Time-Synchronized
Control: Analysis
and Design
Time-Synchronized Control: Analysis and Design
· ·
Dongyu Li Shuzhi Sam Ge Tong Heng Lee
Time-Synchronized Control:
Analysis and Design
DongyuLi ShuzhiSamGe
SchoolofCyberScienceandTechnology DepartmentofElectricalandComputer
BeihangUniversity Engineering
Beijing,China NationalUniversityofSingapore
Singapore,Singapore
TongHengLee
DepartmentofElectricalandComputer
Engineering
NationalUniversityofSingapore
Singapore,Singapore
ISBN978-981-16-3088-0 ISBN978-981-16-3089-7 (eBook)
https://doi.org/10.1007/978-981-16-3089-7
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Toparents,HuiyingandYouningfortheir
companionshipinthejourney,andtomentors
fortheirguidancewithoutreservation
DongyuLi
Toparentsfortheirloveandcontentment
inlife,toJinlanforhercaretothefamilies,
andtofriendsfortheirsupports
ShuzhiSamGe
Tomyfamily,andtosincerefriends
TongHengLee
Preface
In the literature of control science and engineering, we are more concerned with
convergence of the states of any dynamic multi-input-multi-output systems, then
payattentiontoacademicallychallengingandpracticallyrelevantfinite-timeconver-
gence where finite-time control drives the states to converge within a certain time
moment,andfinallysolvetheimportantandcriticalissueinsolvinghoweachstate
elementconvergesasdemandedinmanyaccurate,precise,anddelicateoperations
in many applications including robotic autonomy, manufacturing operations, and
explorationinoceansandspace.
Thismonographdevelopsandintroducesvariousfundamentalandbasicsoftime-
synchronizedcontrolanditsstabilitybecauseofthedemandforpreciseanddedicated
operations in practice. Interconnections with finite-time control and sliding mode
control are explored. The work forges ahead beyond the well-established notions
and outcomes of standard “Finite-Time Stability”, and investigates and develops
resultsandoutcomesforanewer(andinvariousimportantinstances,moreimpactful)
notionof“Time-SynchronizedStability”.Thisworkisorientedtowardsresearchers,
engineers,andstudentswhodedicatethemselvesforthebestcontrolsystemdesign
in practice yet with sound theoretical support by seamlessly integrating or fusing
academicexplorationandengineeringregulations.
Specifically and importantly, under time-synchronized control, all the state
elementsofatargetsystemconverge totheoriginexactly atthesametime,called
time-synchronizedconvergence.Theassociatedtime-synchronizedstabilityisbuilt
ontopof thewell-known standard notion of finite-timestability,butadds toitthe
furthernotionoftime-synchronizedconvergence.Inthismonograph,weunderscore
anddiscoverimportantoutcomesandpropertiesassociatedwithfinite-timestability,
and then define a notion and concept of a control system—ratio persistence. All
of these together contribute to time-synchronized stability. Ratio persistence is an
essentialpropertythatkeepseachpairoftheclosed-loopsystemstateelementsbeing
constant.Notethateventheclassicalproportionalcontrol(Pcontrol)canappropri-
atelyenableacontrolsystemtoberatiopersistent.Thus,Pcontrolcanbeseenasa
veryspecialtypeoftime-synchronizedcontrol,whereitssynchronizedsettlingtime
ist →∞.Ofcourseherein,ourexplorationsandattainedoutcomesaremuchmore
vii
viii Preface
impactfulbeyondthisinconsequence.Theresultsandoutcomesherepertaintoreal-
izingthisratiopersistence,andtime-synchronizedcontrolwithfinite-timestability
aswell.
Time-synchronized control can be viewed as offering coordination of different
states of the system in time for different applications in the sense that, as time
passes,thesystemstateelementsconvergetotheequilibriumwhilealwayspreserving
a constant ratio among them. These unique nature and property make time-
synchronized control highly attractive in providing not only time-synchronized
convergence, but also more nice properties for this interesting time-synchronized
convergencepropertyattainedsuchasasmoothsystemoutput,ashortstatetrajectory,
reducedenergyconsumption,improvedconvergenceaccuracy,amongothers.
Themaincontentofthisbookincludestime-synchronizedstabilityanditsrelevant
Lyapunovtheorems,time-synchronizedcontroldesignfordifferenttypesofsystems
withpracticalconsiderations,andexplorationsintime-synchronizedconsensus.
In Chap. 2, time-synchronized stability, fixed-time-synchronized stability, and
predefined-time stability as well as their respective Lyapunov-like theorems are
proposed.Fixed-andpredefined-time-synchronizedstabilityareregardedasspecial
typesoftime-synchronizedstability.
In Chap. 3, quasi-continuous and continuous time-synchronized sliding modes
are introduced to facilitate the achievement of time-synchronized stability. Their
convergencerate,singularityissue,typesofcontinuityareproperlydiscussed.
In Chaps. 4–6, time-synchronized controllers are proposed for affine systems,
Euler-Lagrangesystems,andgeneralMIMOsystemsundermatchedandunmatched
disturbances, where time-synchronized or fixed-time-synchronized convergence is
achieved.Animportantmatterofsingularityavoidanceissuitablyaddressed.Further,
weintroducetheconceptof“theleastupperboundofsynchronizedsettlingtime”to
accuratelyestimatethesynchronizedsettlingtime.Anextensiontopredefined-time-
synchronizedcontrolisfurtheraddressed.
In Chap. 7, the time-synchronized consensus problem is defined and solved. It
showsthatallthestateelementsofthemulti-agentsystemarecapableofachieving
consensustime-synchronouslywhenthegraphtheoryisproperlyinvokedwiththe
proposedtime-synchronizedconsensuscontroller.
InChaps.8and9,(practical)time-synchronizedcontrolisproposedfordisturbed
spacecraftundermultiplepracticalconstrainswithhardware-in-loopexperiments.
In Chap. 10, pertinent conclusions are drawn with interesting but challenging
possiblefuturedirections.
BuddingandGenesis
Thegenesisandmullingofthismonographywereverymuchinspiredandmotivated
by many excellent scientific works including Linear Controller Design: Limits of
PerformancebyS.BoydandC.Barratt,OptimalControlbyF.L.Lewis,D.Vrabie
Preface ix
andV.L.Syrmos,Slidingmodecontrol:theoryandapplicationsbyC.Edwards,S.
Spurgeon,andmanyexcellentworkspresentedatTCCTWorkshoponCooperative
ControlandMulti-AgentSystemsundertheleadershipofJieChen,Beijing.Aswe
investigated different control performance specifications for multi-agent systems,
we further investigated the description and usage of two different versions of the
signumfunction—theusualstandardversionandanorm-normalizedversion,i.e.one
definedbythesignumelementandtheotherbythestandardunitvectorasillustrated
in Adaptive Neural Network Control of Robotic Manipulators by S. S. Ge, T. H.
LeeandC.J.Harris.Weexploredthatthisnorm-normalizedversionhadthatspecial
property(essentiallyofratiopersistence)toassure,whatwehadtermedatthatinitial
stage,“SimultaneousArrivalToOrigin”(SATO)convergence(despiterathersimple
underlyingmathematicalanalysis,thatisactually,time-synchronizedconvergence).
Motivated by this interesting property, we determined to seek a revisit of existing
outcomesin“Finite-TimeStability”and“SlidingModeControl”toexploreSATO
convergenceindepth.In2018,wehadmanagedtosuccessfullydevelopsomeearly
promisingresultsalongthisline,wheretime-synchronizedcontrolsweredesigned
to achieve time-synchronized convergence for simple first-order systems. In 2019,
wefurtherdevelopedthisworkandmanagedtosynthesizemethodologiesimproving
theoutcomes,wheremoretypesoftime-synchronizedstabilityandmorepractical
control systems were considered. With the journal manuscripts submitted, review
comments came back which additionally benefited our work. It is indeed pleasant
on how all the pieces have now fallen nicely in place; here this book/monograph
is available to all who had expressed their great interest, and also to many others
who,wehopeandtrust,willappreciatethegreatpotentialoftheconceptsandresults
here.Wewelcomeinterestedexcellentindividualstofurtherpushtheboundarywell
beyond.
Pleaseenjoyreading!
Beijing,China DongyuLi
Singapore,Singapore ShuzhiSamGe
Singapore,Singapore TongHengLee
Acknowledgments
Weareheretoextendourgratitudetowardscolleaguesandcollaborators.Wewould
also like to express our sincere appreciation to numerous valuable suggestions,
comments,andmulti-facetedsupportstoourunderstandingandformulationofthe
currentresearchworksasthefoundationforthismonograph,inparticular,from(in
alphabeticalorderoflastnames)
RodrigoAldanaofUniversityofZaragoza,
LindaBushnellofUniversityofWashington,
HuiCaoofXi’anJiaotongUniversity,
XiaoChenofShanghaiInstituteofSatelliteEngineering,
KunCaoofNanyangTechnologicalUniversity,
HuixuDongofNationalUniversityofSingapore,
ShuoDingofNationalUniversityofSingapore,
LeonidFridmanofNationalAutonomousUniversityofMexico,
YanningGuoofHarbinInstituteofTechnology,
YufengGaoofHarbinInstituteofTechnology,
QingleiHuofBeihangUniversity,
WeiHeofUniversityofScienceandTechnologyBeijing,
ZhiminHouofNationalUniversityofSingapore,
WanyueJiangofQingdaoUniversity,
FrankL.LewisofUniversityofTexasatArlington,
JianweiLiuofBeihangUniversity,
ShuaiLiuofShandongUniversity,
ChuanjiangLiofHarbinInstituteofTechnology,
YueyongLvofHarbinInstituteofTechnology,
XiaolingLiangofNationalUniversityofSingapore,
XianLiofQingdaoUniversity,
XingLiuofNorthwesternPolytechnicalUniversity,
GuangfuMaofHarbinInstituteofTechnology,
JunMaofHarvardUniversity,
LorenzoMarconiofUniversityofBologna,
YongduanSongofChongqingUniversity,
XiaodongShaoofBeihangUniversity,
xi
xii Acknowledgments
KengPengTeeofAgencyforScience,TechnologyandResearch(SG),
YanWuofAgencyforScience,TechnologyandResearch(SG),
LihuaXieofNanyangTechnologicalUniversity,
HaoyongYuofNationalUniversityofSingapore,
WeiYouofShanghaiInstituteofSatelliteEngineering,
HaoyangYangofBeihangUniversity,
JianyingZhengofBeihangUniversity,
WeiZhangofShanghaiInstituteofSatelliteEngineering,
YanzhongZhaoofChineseAcademyofSciences,amongothers.
Special thanks towards William Achauer, Anil Chandy, Jasmine Dou,
Bhagyalakkshme from Springer, for their consistent and reliable support and
comments in the process of publishing the book, and towards IEEE for granting
usthepermissiontorevisitmaterialsfromourpublications.
Beijing,China DongyuLi
Singapore,Singapore ShuzhiSamGe
Singapore,Singapore TongHengLee
June2021
