具有未知参数混沌系统的有限时间和固定时间混合函数投影同步.pdf
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1、兰州大学学报(自然科学版),2 0 2 3,5 9(4)8 月Journal of Lanzhou University(Natural Sciences),2023,59(4)/AugustFinite-time and fixed-time hybrid function projection synch-ronization of chaotic systems with unknown parametersLI De-kuiDepartment of Science Teaching,Gansu University of Chinese Medicine(Dingxi Campus)
2、,Dingxi743000,Gansu,ChinaAbstract:Finite-time and fixed-time hybrid function projection synchronization of chaotic systems withunknown parameters were studied in this paper.Based on the Lyapunov stability theorem and synchroni-zation control strategy,two adaptive controllers were constructed to real
3、ize a hybrid function projectionsynchronization of the drive system and response one under the finite-time and fixed-time condition,respectively.The upper bounds of the synchronization time were estimated in the two situations,respec-tively,and we found that the synchronization time of finite-time s
4、ynchronization depended on the initialvalue,but the synchronization time of the fixed-time synchronization was independent of the initial value.All the unknown parameters of the drive system and response system were identified by using the con-structed parameter identification laws.Two numerical exa
5、mples were presented to illustrate the correctnessandeffectivenessoftheresults.Keywords:finite-time synchronization;fixed-time synchronization;hybrid function projection synchroni-zation;parameter identification;synchronization timeCLCnumber:TP273Documentcode:AArticlcalID:0455-2059(2023)04-0512-12D0
6、I:10.13885/j.issn.0455-2059.2023.04.012AMS SubjectClassifications(2010):94A05;34H10;34D06具有未知参数混沌系统的有限时间和固定时间混合函数投影同步李德奎甘肃中医药大学(定西校区)理科教学部,甘肃定西7 4 30 0 0摘要:研究具有未知参数混沌系统的有限时间和固定时间混合函数投影同步.基于Lyapunov稳定性定理和同步控制策略,在有限时间同步和固定时间同步条件下,构造两种自适应控制器,分别实现驱动系统和响应系统的混合函数投影同步.分别估计两种情况下的同步时间上界,发现有限时间同步的同步时间依赖于系统初值,
7、固定时间同步的同步时间不依赖于系统的初值。利用构造的参数辨识法则,准确辩识驱动系统和响应系统的所有未知参数.给出两个数值例子,说明结论的正确性和有效性,关键词:有限时间同步;固定时间同步;混合函数投影同步;参数辨识;同步时间Receiveddate:2022-04-23Found term:Supported by the National Natural Science Foundation of China(11161027);Natural Science Foundation of GansuProvince(21JR1RA259,20JR10RA329);Foundation of
8、Gansu Education Bureau(2020A-191)Biography:LI De-kui(1979-),male,born in Tongwei,Gansu Province,vice professor,master,e-mail:,major-ing inthe theoryand applicationofchaotic system.513parametersLI De-kui:Finite-time and fixed-time hyvbriiunelnchronization of chaotic systems with unknownIn recent deca
9、des the control and synchroniza-tion of chaos and the complex network has beenwidely studied in many disciplines such as chemistry,information science,biology,mathematics,securecommunication,etc.and many research results havebeen obtainedli-,one of the most important ofwhich is that some synchroniza
10、tion patterns havebeen defined and studied,plete synchroniza-tionl-,anti-synchronization,lag synchronization,phase synchronization,function projection synchro-nizationo-,hybrid function projection synchroniza-tion2l,etc.Comparing with others synchronizationpatterns,the hybrid function projection syn
11、chroniza-tion is the most complex one,because of the differ-ent function scaling factors between the differentpairs of state variables of the drive system andresponse system.Due to the complexity of this syn-chronization pattern,applying it to secure communi-cation can make communication information
12、 moresecure and reliable.Hybrid function projection synchronization ofchaotic systems has potential research values,how-ever,almost all studies about it are asymptotic andof infinite-time synchronization by controlling to theresponse systeml2-5,.The hybrid function projectionsynchronization of diffe
13、rent chaotic systems hasbeen studied via Fourier series expansion and adap-tive controlling technique,with the former havingbeen used to deal with uncertain time-varyingparameters.An adaptive control law and six param-eter updating laws have been constructed to makethe states of two different chaoti
14、c systems asymp-totically synchronized based on the Lyapunov stabil-ity theoryl2.Because the scaling factors of hybridprojection synchronization are hardly predictable,the linear feedback control method has been ad-opted to control the different state variables of cha-otic systems onto any desired v
15、aluesl3.Hybridmodified function projection synchronization in twocomplex nonlinear systems with all unknown param-eters has been achieved.In the complex space,theresponse system are asymptotically synchronized tothe drive system,and all of unknown parameters intwo systems have been identified14:hybr
16、id functionprojection synchronization and parameter identifica-tion of different dimension chaotic systems.Basedon the Lyapunov stability theory,an adaptive con-troller has been designed to control the response sys-tem,and thus the state variables of the controlledresponse system and the drive syste
17、m achieved syn-chronization via different function scaling factorsis.The asymptotic synchronization just requiresthat the error system of chaotic systems convergesto zero with time tending to infinity.However,theasymptotic synchronization of the chaotic system isnot reasonable because the life time
18、of machine andhuman is finite;so it is more reasonable to realizesynchronization of chaotic systems in relatively shortfinitetime.In recent years many have studied the finite-time synchronization of chaotic systems.The glob-ally synchronization of the different dimensionalchaotic systemsll,synchroni
19、zation and uncertainparameter identification of the unified chaotic sys-tem,and complete synchronization of chaotic sys-tems with different ordersl1sI have been realized infinite time.The chaos synchronization with timedelay and its application in secure communicationare discussed in finite timel9.T
20、he chaos synchroni-zation application is investigated in wireless sensornetworks20 From the above results we find thatfinite-time synchronization of the chaotic systemscan not only be realized within a given instant,butalso be applied in many domains.In the finite-time synchronization,the upperbound
21、 of the synchronization time depends on theinitial values of chaotic systems,such that differentinitial states will produce different convergencespeeds.It is difficult to get the initial values of thechaotic systems in practical situations and,there-fore,it is very inconvenient to design a controlle
22、rand estimate the synchronization time.In order tosolve this problem,a fixed-time synchronizationcontrol has recently been proposed,which can notonly realize the synchronization of the chaotic sys-tems in the settling time but also that the time doesnot depend on the initial values of chaotic sys-te
23、ms(2-2,According to the actual situation of the chaoticsystems,we may select the fixed-time pattern or thefinite-time one to realize the synchronization of thechaotic systems.However,the finite-time or fixed-time synchronization are studied mainly in neuraland complex networks23-27.In reference 27 t
24、heauthors have studied the cluster synchronization of aclass of the nonlinearly coupled delayed neural net-works in both finite-time and fixed-time situations.According to the Lyapunov stability theory and pin-projection synchronization in finite time T.andresponsesystem(2)realizehybridfunctionunkno
25、wnparameteystem(1)atecontrollerandnationlawoftheRemark 2Our goal is to design an appropri-synchronization.finite-time or fixed-time hybrid function projectionsystem(1)and the response system(2)realize thelimy(t)-H(t)x(t)J-lim e(t)=0,then the drivecan tend to zero within the settling time T,that isIf
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