基于自适应滑模控制的分数阶蔡氏电路系统动力学分析与控制
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摘要
为了研究整数阶电路系统的动态行为,国内外学者做了非常巨大的努力,得出了许多重要的结论。然而,在现实生活中,更多的系统是分数阶系统。因此,研究分数阶蔡氏电路系统的动力学行为就变得非常的前沿和有意义。这篇文章主要研究对象是三阶分数阶蔡氏电路系统,通过分数阶劳斯-赫尔维兹判据,李雅普诺夫稳定性判断方法以及矩阵理论等推导出分数阶蔡氏电路系统的渐近稳定性的充分条件以及自适应控制器的选取条件。最后通过数值模拟的方法,验证了理论的有效性和合理性。
In order to study the dynamic behavior of integer order system,scholars both in china and abroad have made great efforts and reached many important conclusions.However,in real life,the more existence is the fractional-order system.Therefore,The study of dynamic behavior of fractional-order Chua's circuit system becomes very forward and meaningful.The main research object of this paper is the three dimensional fractional-order chua′s circuit system,through the Routh-Hurwitz criterion,Lyapunov stability judgment method and matrix theory derived the sufficient condition of the asymptotic stability of the Chua's circuit system and the selection of adaptive controller condition.Finally,the validity and rationality of the theory are verified by numerical simulation.
In order to study the dynamic behavior of integer order system,scholars both in china and abroad have made great efforts and reached many important conclusions.However,in real life,the more existence is the fractional-order system.Therefore,The study of dynamic behavior of fractional-order Chua's circuit system becomes very forward and meaningful.The main research object of this paper is the three dimensional fractional-order chua′s circuit system,through the Routh-Hurwitz criterion,Lyapunov stability judgment method and matrix theory derived the sufficient condition of the asymptotic stability of the Chua's circuit system and the selection of adaptive controller condition.Finally,the validity and rationality of the theory are verified by numerical simulation.
引文
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[13]赵小国,阎晓妹,孟欣.基于RBF神经网络的分数阶混沌系统的同步[J].复杂系统与复杂性科学,2010,07(1):40-46.Zhao xiaoguo,Yan xiaomei,Meng xin.Synchronization of fractional order chaotic systems based on RBF neural networks[J].Complex systems and complexity science,2010,07(1):40-46.
[14]Liu H,Li G,Zhang X,et al.Generation of fractional-order multi-scroll chaotic systems based on Chua's circuits[C]Control Conference.IEEE,2016:808-812.
[15]Kingni S T,Pham V T,Jafari S,et al.Three-dimensional chaotic autonomous system with a circular equilibrium:analysis,circuit implementation and its fractional-order form[J].Circuits Systems&Signal Processing,2016,35(6):1933-1948.
[16]Sun Q,Xiao M,Tao B.Local bifurcation analysis of a fractional-order dynamic model of genetic regulatory networks with delays[J].Neural Processing Letters,2017,47(3):1-12.
[2]谢永兴,胡云安,林涛,等.蔡氏混沌电路联合仿真方法研究[J].仪表技术,2016(1):11-14.Xie Yongxing,Hu Yunan,Lin Tao,et al.Study on the combined simulation method of chua's chaotic circuit[J].Instrumentation Technology,2016(1):11-14.
[3]闵富红,彭光娅,叶彪明,等.无感蔡氏电路混沌同步控制实验[J].实验技术与管理,2017(2):43-46.Min Fuhong,Peng Guangya,Ye Bioming,et al.Chaotic synchronization control experiment of senseless caishi circuit[J].Experimental Technology and Management.,2017(2):43-46.
[4]Bao B,Wang N,Chen M,et al.Inductor-free simplified Chua’s circuit only using two-op-amp-based realization[J].Nonlinear Dynamics,2016,84(2):511-525.
[5]Rocha R,Ruthiramoorthy J,Kathamuthu T.Memristive oscillator based on Chua’s circuit:stability analysis and hidden dynamics[J].Nonlinear Dynamics,2017,88(4):2577-2587.
[6]Kengne J.On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity:occurrence of multiple attractors[J].Nonlinear Dynamics,2016:1-13.
[7]Voliansky R,Sadovoy A.Chua's circuits synchronization as inverse dynamic's problem solution[C]Problems of Infocommunications Science and Technology.IEEE,2017:171-172.
[8]Sarkar S S D,Chakraborty S.Nonlinear dynamics of a class of derivative controlled Chua’s circuit[J].International Journal of Dynamics&Control,2017,Accepted(1701):1-8.
[9]Liao X.Dynamical behavior of chua's circuit with lossless transmission line[J].IEEE Transactions on Circuits&Systems I Regular Papers,2016,63(2):245-255.
[10]杨洪勇,徐邦海,刘飞,等.分数阶多智能体系统的时延一致性[J].复杂系统与复杂性科学,2013,10(3):81-85.Yang Hongyong,Xu Banghai,Liu Fei,et al.Time delay consistency of fractional multi-agent system[J].Complex System and Complexity Science,2013,10(3):81-85.
[11]徐磊,张成芬,高金峰.分数阶Chua系统中的混沌现象及其同步控制[J].复杂系统与复杂性科学,2007,4(4):45-50.Xu Lei,Zhang Chengfen,Gao Jinfeng.Chaos and its synchronization control in fractional Chua system[J].Science of Complex Systems and Complexity,2007,4(4):45-50.
[12]高金峰,张成芬.基于非线性观测器实现一类分数阶混沌系统的同步[J].复杂系统与复杂性科学,2007,4(2):50-55.Gao Jinfeng,Zhang Chengfen.Synchronization of a class of fractional order chaotic systems based on nonlinear observers[J].Science of Complex Systems and Complexity,2007,4(2):50-55.
[13]赵小国,阎晓妹,孟欣.基于RBF神经网络的分数阶混沌系统的同步[J].复杂系统与复杂性科学,2010,07(1):40-46.Zhao xiaoguo,Yan xiaomei,Meng xin.Synchronization of fractional order chaotic systems based on RBF neural networks[J].Complex systems and complexity science,2010,07(1):40-46.
[14]Liu H,Li G,Zhang X,et al.Generation of fractional-order multi-scroll chaotic systems based on Chua's circuits[C]Control Conference.IEEE,2016:808-812.
[15]Kingni S T,Pham V T,Jafari S,et al.Three-dimensional chaotic autonomous system with a circular equilibrium:analysis,circuit implementation and its fractional-order form[J].Circuits Systems&Signal Processing,2016,35(6):1933-1948.
[16]Sun Q,Xiao M,Tao B.Local bifurcation analysis of a fractional-order dynamic model of genetic regulatory networks with delays[J].Neural Processing Letters,2017,47(3):1-12.