Adaptive control of a two-scroll novel chaotic system with a quartic nonlinearity

机译：具有二次非线性的两卷新型混沌系统的自适应控制

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This paper proposes a two-scroll novel 3-D chaotic system with a quartic nonlinearity and devises an adaptive control law for globally stabilizing the system when the system parameters are unknown. First, this paper derives fundamental qualitative properties of the new chaotic system such as dissipativity, symmetry, invariance, Lyapunov exponents and Lyapunov dimension. The phase portraits of the novel chaotic system are shown using MATLAB. Next, this paper uses adaptive control theory and Lyapunov stability theory to derive an adaptive feedback control law for globally stabilizing the novel chaotic system for all initial conditions. The main result is proved with the help of Lyapunov stability theory. Adaptive control results are validated by MATLAB simulations.

机译：提出了一种具有二次非线性的两辊新型3-D混沌系统，并设计了一种自适应控制律，用于在系统参数未知的情况下全局稳定系统。首先，本文推导了新混沌系统的基本定性性质，如耗散性，对称性，不变性，李雅普诺夫指数和李雅普诺夫维数。使用MATLAB显示了新型混沌系统的相图。接下来，本文使用自适应控制理论和Lyapunov稳定性理论来推导自适应反馈控制律，以在所有初始条件下全局稳定新型混沌系统。借助李雅普诺夫稳定性理论证明了主要结果。自适应控制结果通过MATLAB仿真进行了验证。

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来源
《2014 International Conference on Science Engineering and Management Research》|2014年|1-6|共6页
会议地点 Chennai(IN)
作者
Vaidyanathan Sundarapandian; Madhavan Kavitha;
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作者单位

RD Centre, Vel Tech Univ., Chennai, India;

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原文格式 PDF
正文语种 eng
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关键词
Lyapunov methods; adaptive control; chaos; feedback; mathematics computing; nonlinear systems; stability; 3D chaotic system; Lyapunov dimension; Lyapunov exponents; Lyapunov stability theory; MATLAB simulations; adaptive control; adaptive feedback control law; dissipativity exponents; invariance exponents; quartic nonlinearity; symmetry exponents; system global stabilization; system parameters; two-scroll novel chaotic system; Adaptive control; Chaotic communication; Lyapunov methods; Mathematical model; Numerical simul;

机译：Lyapunov方法;自适应控制;混沌;反馈;数学计算;非线性系统;稳定性; 3D混沌系统; Lyapunov维度; Lyapunov指数; Lyapunov稳定性理论; MATLAB模拟;自适应控制;自适应反馈控制律;耗散指数;不变指数;四次非线性;对称指数;系统全局稳定;系统参数;两卷新型混沌系统;自适应控制;混沌通信; Lyapunov方法;数学模型;数值模拟;

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4. Adaptive control of a two-scroll novel chaotic system with a quartic nonlinearity [C] . Vaidyanathan Sundarapandian, Madhavan Kavitha International Conference on Science Engineering and Management Research . 2014

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5. Robust and adaptive control of chaotic systems via computational intelligence. [D] . Lu, Zhao. 2004

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6. Design of Adaptive-Robust Controller for Multi-State Synchronization of Chaotic Systems with Unknown and Time-Varying Delays and Its Application in Secure Communication [O] . Ali Akbar Kekha Javan, Afshin Shoeibi, Assef Zare, 2021

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8. Prediction and control of chaotic processes using nonlinear adaptive networks. [R] . Jones, R. D., Barnes, C. W., Flake, G. W., 1990

机译：非线性自适应网络对混沌过程的预测与控制。

Adaptive control of a two-scroll novel chaotic system with a quartic nonlinearity

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