广义分数阶Sprott-C混沌系统的有限时间滑模同步
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摘要
利用分数阶有限时间稳定性理论,通过构造合适的分数阶滑动模态超曲面,设计一种含有有限时间控制作用的分数阶控制器,以实现广义Sprott-C驱动-响应系统的滑模同步控制.结合自适应控制策略,利用参数更新律对未知参数和扰动上界进行准确估计,并选取适当的控制和系统参数,利用MATLAB数值仿真,验证所得结果的正确性和有效性.
By using the fractional-order finite-time stability theory,and constructing a proper fractional-order sliding-mode hyper surface,a fractional-order controller with finite-time control was designed to realize the sliding-mode synchronization control of generalized drive-response Sprott-C systems.Combined with adaptive control strategy,the unknown parameters and the upper bounds of disturbance were accurately estimated by using parameter update laws.The correctness and validity of the results were verified by MATLAB numerical simulation with appropriate control and system parameters.
By using the fractional-order finite-time stability theory,and constructing a proper fractional-order sliding-mode hyper surface,a fractional-order controller with finite-time control was designed to realize the sliding-mode synchronization control of generalized drive-response Sprott-C systems.Combined with adaptive control strategy,the unknown parameters and the upper bounds of disturbance were accurately estimated by using parameter update laws.The correctness and validity of the results were verified by MATLAB numerical simulation with appropriate control and system parameters.
引文
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[2]BALEANU D,GUNENC Z B,TENREIRO M J A.New Trends in Nanotechnology and Fractional Calculus Application[M].London:Springer,2010.
[3]YOUSRI D A.ABDELATY A M,SAID L A,et al.Parameter Identification of Fractional-Order Chaotic Systems Using Different Meta-Heuristic Optimization Algorithms[J].Nonlinear Dynamics,2019,95(3):2491-2542.
[4]毛北行.分数阶Newton-Leipnik混沌系统滑模同步的两种方法[J].吉林大学学报(理学版),2018,56(3):708-712.(MAO Beixing.Two Methods for Sliding Mode Synchronization of Fractional-Order Newton-Leipnik Chaotic Systems[J].Journal of Jilin University(Science Edition),2018,56(3):708-712.)
[5]YANG Xujun,LI Chuandong,HUANG Tingwen,et al.Mittag-Leffler Stability Analysis of Nonlinear FractionalOrder Systems with Impulses[J].Applied Mathematics and Computation,2017,293(15):416-422.
[6]NORELYS A C,MANUEL A D M,JAVIER A G.Lyapunov Functions for Fractional Order Systems[J].Communications in Nonlinear Science and Numerical Simulation,2014,19(9):2951-2957.
[7]MOHAMMADZADEH A,GHAEMI S.A Modified Sliding Mode Approach for Synchronization of FractionalOrder Chaotic/Hyperchaotic Systems by Using New Self-structuring Hierarchical Type-2Fuzzy Neural Network[J].Neurocomputing,2016,191:200-213.
[8]MOHADESZADEH M,DELAVARI H.Synchronization of Fractional-Order Hyper-Chaotic Systems Based on a New Adaptive Sliding Mode Control[J].International Journal of Dynamics and Control,2017,5(1):124-134.
[9]SAMPATH S,VAIDYANATHAN S.Hybrid Synchronization of Identical Chaotic Systems via Novel Sliding Control Method with Application to Sampath Four-Scroll Chaotic System[J].Control Theory and Technology,2016,9(1):221-235.
[10]MEHRAN T,SAEED B.Synchronization of the Chaotic Fractional-Order Genesio-Tesi Systems Using the Adaptive Sliding Mode Fractional-Order Controller[J].Journal of Control,Automation and Electrical Systems,2018,29(1):15-21.
[11]AHAMAD H,MOJTABA H,DUMITRU B.On the Adaptive Sliding Mode Controller for a Hyperchaotic Fractional-Order Financial System[J].Physica A,2018,497:139-153.
[12]MUTHUKUMAR P,BALASUBRAMAMIAM P,RATHNAVELU K.Sliding Mode Control Design for Synchronization of Fractional Order Chaotic Systems and Its Application to a New Cryptosystem[J].International Journal of Dynamics and Control,2017,5(1):115-123.
[13]WANG Chenhui.Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems[J].Advances in Mathematical Physics,2018(1):1-9.
[14]YIN Chun,CHENG Yuhua,ZHONG Shouming,et al.Fractional-Order Switching Type Control Law Design for Adaptive Sliding Mode Technique of 3D Fractional-Order Nonlinear Systems[J].Complexity,2016,21(6):363-373.
[15]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):110-118.(LI Te,YUAN Jianbao,WU Ying.A Method of Adaptive Sliding Mode Control for Synchronization of One Class of Uncertain Fractional-Order Chaotic Systems[J].Journal of Dyanmics and Control,2017,15(2):110-118.)
[16]ZHAO Yuhan,WU Ranchao.Chaos and Synchronization of a New Fractional Order System with Only Two Stable Equilibria[J].International Journal of Dynamical Systems and Differential Equations,2016,6(3):187-202.
[17]PODLUBNY I.Fractional Differential Equation[M].New York:Academic Press,1999.
[18]LI Yan,CHEN Yangquan,PODLUBNY I.Stability of Fractional-Order Nonlinear Dynamic Systems:Lyapunov Direct Method and Generalized Mittag-Leffler Stability[J].Computers and Mathematics with Applications,2010,59(5):1810-1821.
[19]刘恒,李生刚,孙业国,等.带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊同步控制[J].物理学报,2015,64(7):070503-1-070503-9.(LIU Heng,LI Shenggang,SUN Yeguo,et al.Adaptive Fuzzy Synchronization for Uncertain Fractional-Order Chaotic Systems with Unknown Non-symmetrical Control Gain[J].Acta Physica Sinica,2015,64(7):070503-1-070503-9.)