一类分数阶超混沌系统修正函数投影同步的滑模控制
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摘要
对一类具有未知参数的分数阶超混沌系统的修正函数投影同步进行研究.通过设计响应系统的补偿器,进而得到修正函数投影同步的误差系统.基于自适应滑模控制理论和分数阶微分系统的稳定性理论,设计了一种自适应同步的控制方案.通过选取自适应滑模控制器以及参数自适应控制率,最终实现了驱动系统和响应系统修正函数投影同步,并可以对不确定参数进行估计.最后针对结论,以分数阶超混沌L(u|¨)系统为例,利用Adams-Bashfortlh-Moultom算法进行数值仿真,其结果说明了该方法的有效性和可行性.
Modified function projective synchronization for a class of fractional-order hyper chaotic system with unknown parameters is investigated.By designing the compensator of the response system,the error system of modified function projective synchronization is obtained.Based on the theory of adaptive sliding mode control and the stability theory of fractional-order differential systems,an adaptive projective synchronization control scheme is designed.By selecting the adaptive sliding mode controller and adaptive control laws of the parameter,the Modified function projective synchronization between the master system and the response system is implemented,and the uncertain parameters of the master system could be estimated.Finally,the fractional-order hyper chaotic L(u|¨) system that is taken as an example with simulations via Adams-Bashforth-Moultom algorithm is used to demonstrate the validity and feasibility of the proposed results.
Modified function projective synchronization for a class of fractional-order hyper chaotic system with unknown parameters is investigated.By designing the compensator of the response system,the error system of modified function projective synchronization is obtained.Based on the theory of adaptive sliding mode control and the stability theory of fractional-order differential systems,an adaptive projective synchronization control scheme is designed.By selecting the adaptive sliding mode controller and adaptive control laws of the parameter,the Modified function projective synchronization between the master system and the response system is implemented,and the uncertain parameters of the master system could be estimated.Finally,the fractional-order hyper chaotic L(u|¨) system that is taken as an example with simulations via Adams-Bashforth-Moultom algorithm is used to demonstrate the validity and feasibility of the proposed results.
引文
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[18]Lii J H,Chen G R.A new chaotic attractor coined[J].Int J Bifurcation&Chaos(S0218-1274),2002,12(3):659-661.
[2]Yu Y G,Li H X.Adaptive generalized function projective synchronization of uncertain chaotic systems[J].Nonlinear Analysis:Real World Applications,2010,11(4):2456-2464.
[3]Sebastian K,Sabir M.Adaptive modified function projective synchronization between hyper ch aotic Lorenz system and hyper chaotic Lii system with uncertain parameters[J].Physics Letters A,2009,373(41):3743-3748.
[4]黄春,吴艳敏,方洁.受扰不确定混沌系统的降阶修正函数投影同步[J].数学的实践与认识,2014,44(02):216-222.
[5]Radwan A G,Moaddy K,Salama K N,et al.Control and switching synchronization of fractional order chaotic systems using active control technique[J].Journal of Advanced Research,2014,5(1):125-132.
[6]李东,张兴鹏,胡玉婷,等.参数不确定的不同分数阶的混沌系统的自适应同步[J].西南大学学报(自然科学版),2015,37(11):69-76.
[7]Zhang K,Wang H,Fang H.Feedback control and hybrid projective synchronization of a frac tionalorder newton-leiplink system[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(1):317-328.
[8]吴学礼,刘杰,张建华,等.基于不确定性变时滞分数阶超混沌系统的滑模自适应鲁棒的同步控制[J].物理学报,2014,63(16):160507-1-7.
[9]李特,袁建宝,吴莹.一类不确定分数阶混沌系统同步的自适应滑模控制方法[J].动力学与控制学报,2017,15(2):2235-2239.
[10]Mohammad P A,Mohammad E A.A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances[J].Applied Mathematics and Computation,2012,218:5757-5768.
[11]杨红叶,肖剑,马珍珍.部分线性的分数阶混沌系统的修正函数投影同步[J].物理学报,2013,62(18):180505-1-7.
[12]董俊,张广军,姚宏,等.异结构的分数阶超混沌系统函数投影同步及参数辨识[J].电子与信息学报,2013,35(6):1371-1375.
[13]耿彦峰,王立志.一类分数阶超混沌系统的修正函数投影同步[J].宁夏大学学报,2017,42(1):39-45.
[14]孟晓玲,程春蕊.一类分数阶混沌系统的修正函数投影同步[J].湖北大学学报(自然科学版),2018,40(3):232-236.
[15]Duarte-Mermoud M A,Aguila-Camacho N,Gallegos J A,et al.Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems[J].Commun Nonlinear Sci&Numer Simul,2014,22(1/3):650-659.
[16]Li Y,Chen Y Q,Podlubny I.Stability of fractional-order nonlinear dynamic systems:Lyapunov direct method and generalized Mittag-Leffler stability[J].Comput&Math Appli,2010,59(5):1810-1821.
[17]吴强,黄建华.分数阶微积分[M].北京:清华大学出版社,2016.
[18]Lii J H,Chen G R.A new chaotic attractor coined[J].Int J Bifurcation&Chaos(S0218-1274),2002,12(3):659-661.