基于自适应重复学习的不确定多涡卷混沌系统同步控制
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摘要
基于滞环函数提出一种参数可调的多涡卷混沌系统构造方法.针对复杂不确定性系统,综合利用自适应神经网络和重复学习控制方法设计一种自适应重复学习同步控制器;利用自适应重复学习控制方法对周期时变参数化不确定性进行处理;对函数型不确定性利用神经网络逼近技术进行补偿;设计鲁棒学习项对神经网络逼近误差和扰动上界进行估计;通过构造类Lyapunov复合能量函数证明了同步误差学习的收敛性.仿真结果验证了所提出方法的有效性.
Based on hysteresis functions, a kind of multi-scroll chaos systems constructing method is proposed, parameters of which can be adjusted. For a class of chaotic systems with complicated uncertainties, a kind of adaptive repetitive learning synchronization controller is presented by combining the adaptive neural network method and the repetitive learning scheme. The difficulty from periodic time-varying parametric uncertainties are overcomed by using the adaptive repetitive learning method scheme, while the function uncertainties are compensated by using the neural approximation technique. The robust learning term is designed to estimate the upper bounds of neural approximation error and the disturbance. A Lyapunovlike function is constructed to prove the convergence of synchronization errors. Simulation results show the effectiveness of the proposed adaptive repetitive learning synchronization scheme.
Based on hysteresis functions, a kind of multi-scroll chaos systems constructing method is proposed, parameters of which can be adjusted. For a class of chaotic systems with complicated uncertainties, a kind of adaptive repetitive learning synchronization controller is presented by combining the adaptive neural network method and the repetitive learning scheme. The difficulty from periodic time-varying parametric uncertainties are overcomed by using the adaptive repetitive learning method scheme, while the function uncertainties are compensated by using the neural approximation technique. The robust learning term is designed to estimate the upper bounds of neural approximation error and the disturbance. A Lyapunovlike function is constructed to prove the convergence of synchronization errors. Simulation results show the effectiveness of the proposed adaptive repetitive learning synchronization scheme.
引文
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[2]Sun F,Zhao Y,Zhou T.Identify fully uncertain parameters and design controller based on synchronization[J].Chaos Solitons and Fractals,2007,34(5):1677-1682.
[3]Park J H.Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter[J].Chaos Solitons and Fractals,2007,34:1552-1559.
[4]Sun M X,Ge S S.Adaptive repetitive control for a class of nonlinearly parametrized systems[J].IEEE Trans on Automatic Control,2006,51(10):1684-1867.
[5]Xu J X,Yan R.On repetitive learning control for periodic tracking tasks[J].IEEE Trans on Automatic Control,2006,51(11):1842-1848.
[6]Yu M,Ye X D,Qi D L.Robust adaptive repetitive learning control for a class of time-varying nonlinear systems with unknown control direction[J].J Control Theory Appl,2013,11(3):336-342.
[7]Zhu Q,Xu J X,Yang S P,et al.Adaptive backstepping repetitive learning control design for nonlinear discretetime systems with periodic uncertainties[J].Int J of Adaptive Control and Signal Processing,2015,29(4):524-535.
[8]Xu J X,Yan R.Synchronizatioan of chaotic systems via learning control[C].The 8th Int Conf on Control,Automation,Robotics and Vision.Kunming:Institute of Electrical and Electronics Engineers Inc.2004:631-636.
[9]Song Y,Yu X,Chen G,et al.Time delayed repetitive learning control for chaotic systems[J].Bifurcation and Chaos,2002,12(5):1057-1065.
[10]张友安,余名哲,吴华丽.基于自适应神经网络的分数阶混沌系统滑模同步[J].控制与决策,2015,30(5):882-886.(Zhang Y A,Yu M Z,Wu H L.Sliding mode synchronization of fractional-order chaotic systems based on adaptive neural network[J].Control and Decision,2015,30(5):882-886.)
[11]Chen M,Zhou D,Shang Y.A simple time-delayed method to control chaotic systems[J].Chaos Solitons and Fractals,2004,22(5):1117-1125.
[12]Sun Y P,Li J M,Wang J A,et al.Generalized projective synchronization of chaotic systems via asaptive learing control[J].Chinese Physics B,2010,19(2):020505.
[13]Xu J X,Yan R.Synchronization of chaotic systems via learning control[J].Int J of Bifurcation and Chaos,2005,15(12):4035-4041.
[14]吴自忠,邝钰.多涡卷混沌系统的广义同步控制[J].物理学报,2009,58(10):6823-6827.(Wu Z Z,Kuang Y.General synchronization control of multi-scroll chaotic systems[J].Acta Physica Sinica,2009,58(10):6823-6827.)