基于状态反馈控制和观测器的记忆电阻Murali-Lakshmanan-Chua电路混沌自适应同步
State Feedback Control and Observer Based Adaptive Synchronization of Chaos in a Memristive Murali-Lakshmanan-Chua Circuit
摘要：
本文研究了记忆电阻Murali-Lakshmanan-Chua电路中混沌的控制与同步。该电路由本作者在2013年介绍，基本上是一个具有两个不连续边界的非光滑系统，因为它具有通量控制的有源忆阻器作为其非线性元件。虽然混沌的控制已经使用状态反馈技术的影响，自适应同步的概念和基于观测器的方法已被用来实现混沌的同步。这两种技术都是基于状态空间表示理论，这是众所周知的控制工程领域。正如我们在此电路的早期工作中，我们已经推导出庞加莱不连续映射（PDM）和零时间不连续映射（ZDM）的校正，这两个都是实现非光滑系统的真实动力学必不可少的。进一步构造了基于状态空间表示标准形式的观测器和控制器，建立了Luenberger观测器，推导了实现状态反馈控制的控制器增益向量，计算了开关反馈增益矩阵，最后进行了参数估计，实现了基于观测器的自适应同步。通过数值模拟得到的结果包括时间图、相图、参数估计以及误差图和相图的收敛性。
英文摘要：
In this paper we report the control and synchronization of chaos in a Memristive Murali-Lakshmanan-Chua circuit. This circuit, introduced by the present authors in 2013, is basically a non-smooth system having two discontinuity boundaries by virtue of it having a flux controlled active memristor as its nonlinear element. While the control of chaos has been effected using state feedback techniques, the concept of adaptive synchronization and observer based approaches have been used to effect synchronization of chaos. Both of these techniques are based on state space representation theory which is well known in the field of control engineering. As in our earlier works on this circuit, we have derived the Poincaré Discontinuity Mapping (PDM) and Zero Time Discontinuity Mapping (ZDM) corrections, both of which are essential for realizing the true dynamics of non-smooth systems. Further we have constructed the observer and controller based canonical forms of the state space representations, have set up the Luenberger observer, derived the controller gain vector to implement state feedback control and calculated the gain matrices for switch feed back and finally performed parameter estimation for effecting observer based adaptive synchronization. Our results obtained by numerical simulation include time plots, phase portraits, estimation of the parameters and convergence of errors graphs and phase plots showing complete synchronization.
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