No 8-4 有限时间同步,林美丽课程论文.docx

H3.假设外界的扰动"(x)是有界的，即存在正常敷办,使用Ild(XJ)I钺.定义澳变e=x-F%=-a%=/7-/,则澳差系统为e=f(x)-g(y)+F(x)a-G(y+d(x,t)-u(t,x)(3)我们的目标是实现主-从系挽的有限时间同步，下面先给出有限时间定的假念.定义1.考虑如下动力系统x(t)=f(x)若存在一个正借败了，使用!M=且当年7时，IlM)Il=0,则称系线W)=()为有限时间定的.我们的目的是找寻合适的限制,使得主系统和从系统的轨线和y(O,系统数和估计数小，和之力澜*3r1.>rswIka)-M川=。,Ia-<M=()，|6-Ao=o(4)系线(1)和(2)在(4)意义下的混沌同步即为澳差系统(3)在原点的定性.因此，可以通过选取合适的限制函敷*/)和收更新率，对误差系统(3)进行调整，以使主系统(1)和从系统(2)达到同步，且识别未知数.为了得到同步结果，我In先皓出两个引理.引理1：假如存在常数c>0.0<"<,使用连续正定函效/。)清寒下面的不等式V(t)-cV(t)tV>O,V(n)>O.那么，对于随意给定的r。，M(1) V",(V,-,(ro)-c(l-77)(-ro).or<1.(2) V>rpv0)=O,这里乙=%+C(I-V)Bl三2>beR.O<q<,都有(网+|町e+坪.那么，我f有下面结果.定理：若主-从系线(1)-(2)就上述假设HlT3,并且滴意下列条件1 .选取限制M(X)=lf+,e+F(x)'a-G(y)'其中用42B+/?./7=-G(y+,'eflX<r<2则主-从系统(IAQ)可以在有限时间达到同步,同步时间为1.=/且此时系豌的未知数/可分期由之方IR别.证明：JSW1.yapunov函数为1.1 rIr1rv=2e。+万，。“+外eA则V沿着囊差系统(4)的轨线对时间的导致为V=er-et'a-efi'=e(f(x)-g(y)+F(x)a-G(y)+(l(x,t)-u(t,x)-ea'a-et'=e(/(X)-g(x)+er(g(x)-g(y)+eF(X)(Ct-d)-erG(y)(-jff)+erd(x,0-e'(kle+i,三+<f2e)-eara-e'-Ml由上述假设H1-H3,可将VH+H2+eF(x)(a-a)-e,Gy-1)+&H一/(kte+刈2+H?。)-eJd-e；B由式(6)-(7)可将v-eYkIrzyk1=-(H2)i-(k2)-(92)i由弓I理2可将v-叫才)-Z-%="(H1+lkJI,+h2>1=-25/这里2由祠限时间程定性理论，可以内到澳差系统(4)为M限时间一定的.故主-从系观的未知»“7在同步限制中可分别由识别.且由引理1可密，谀差I-Il-系观可以在有限时间达到同步，同步时间为丈=小/2-(-f)'注11由于1.ipsohitz条件比较难于It证，常用式二)在R上对2的连续借导收来代明注2：若在限制及能数更新率中(M)则当e时隈制iB"(r.)->>,敷更新率fg8.所以若出现此情形，在仿真过程中，以来代M+£工，其中，为很小的一个正常败IleIl3.敷值仿A利用*Me进行值仿真险证H阅论结果.考虑以海沌Hyball系纥为主系统，其状态方程为'%、X2X2-sinx1-1.942,O+Xysin.r1COSX1OOX2OO、OCOSAu'4(xj)'+d2(x,t)HQ，从系鼓为R6ler系筑'f><2+y't。YAw(t)yjbh+027°y2O/7,+m,(j)°)J?JU(XJb选取未知今数a,=0,25,2=-O.7,3=5.13,51=-l,jff,=0.2./7,=-7,外界扰动d(dl.d2,d3)1=(0.2sin4/.O.I¾sinf+0.1cos3t,O.1isin2t)rt借fte=IOT,r=l系统构值为(.tl,x2,x,/=(i.i)r,(yl,y1,y9)'=(-1,2,-1)7,(a1.a2,j)r=(0.5,l,1.5)r,(综氏,=(1,2.3)、且由图1-2我们可以招到混沌吸引子的界为-3<xl<3.-5<<5,0<<11.所以同M26,(NY(,)-g(x)=-sinxl-xlI=yx;+(-sin.rl-.rl)"+(-1.942-xlx,-0.2):36.-1.942-X1X1-0.2JOOOIg(X)-g(,H=100x-y<ll.5.v-y.x3Oxl选取勺=13.刈=4(),限制收更新率为M1=13e+“，=13e,+今+x；Sin.r1cosld1+.r,d,-x,klIlellu,=13e,+i+p+cosx1,-y1,忖Mle+乙IkllOXSinXlCOSXlO'OX,OOOCoSXI,r-y2->o“=oy,ojj-Aj.Oo'->J闷且由定理可将，估计PJ步时间”16.0854.数值仿JUa果如图所示.图3是系统(1)和(2)的同步襄差曲线.BB4-5系统(1)和(2)中未知B敷与估计我的索差曲线，图68给出了系筑(1)的未知期改与估计套数图9-11给出了系姚(2)的未知ft与估计参数.由同步谀差图可知，两个系统IS过有限时间(10.5.)能实现同步，这就证明白上述同步方法在实现混沌系统(1)和(2)的同步和未知数叔别时是球的.ffl1混沌吸引子在Al-平面上的投影S2混沌吸引子在M-冬平面上的投影图3混沌flyball系统-混沌R63r系统同步溪差«4iRMflybll系旋中*三«5震沌R5I”系统中BiU1.,=6-QS61示肱%,实线赛示估计Q匕BB7%,实H示估计敷W图9如吟#*实线表示估计.nio虚线我示*a.实疑我示估计*A图8*««"«，实线我示估计敷公S11AMtMA,实线访估计"«A4.结论本文基于有限时间稔定理论，实现了异结构混浊系统的有隈时间同步.并且分别给出主-从系烧中未知X的参数更新律.GenMio-Tsi和Rotsler系跳的仿真栽明，系统在有限时间达到同步，且末1我在有限时间内可由B数更新律IR弱，”证了该方法的有效性.“姬1 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