兰州大学学报（自然科学版），2023，59(4）／8月JournalofLanzhouUniversity(NaturalSciences),2023,59(4)/AugustFinite-timeandfixed-timehybridfunctionprojectionsynch-ronizationofchaoticsystemswithunknownparametersLIDe-kuiDepartmentofScienceTeaching,GansuUniversityofChineseMedicine(DingxiCampus),Dingxi743000,Gansu,ChinaAbstract:Finite-timeandfixed-timehybridfunctionprojectionsynchronizationofchaoticsystemswithunknownparameterswerestudiedinthispaper.BasedontheLyapunovstabilitytheoremandsynchroni-zationcontrolstrategy,twoadaptivecontrollerswereconstructedtorealizeahybridfunctionprojectionsynchronizationofthedrivesystemandresponseoneunderthefinite-timeandfixed-timecondition,respectively.Theupperboundsofthesynchronizationtimewereestimatedinthetwosituations,respec-tively,andwefoundthatthesynchronizationtimeoffinite-timesynchronizationdependedontheinitialvalue,butthesynchronizationtimeofthefixed-timesynchronizationwasindependentoftheinitialvalue.Alltheunknownparametersofthedrivesystemandresponsesystemwereidentifiedbyusingthecon-structedparameteridentificationlaws.Twonumericalexampleswerepresentedtoillustratethecorrectnessandeffectivenessoftheresults.Keywords:finite-timesynchronization;fixed-timesynchronization;hybridfunctionprojectionsynchroni-zation;parameteridentification;synchronizationtimeCLCnumber:TP273Documentcode:AArticlcalID:0455-2059(2023)04-0512-12D0I:10.13885/j.issn.0455-2059.2023.04.012AMSSubjectClassifications(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743000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，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...
