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Delta算子框架下混沌系统的自适应滑模控制

李惠1, 郑柏超1,2, 吴跃文1   

  1. 1. 南京信息工程大学自动化学院, 南京 210044;
    2. 江苏省大气环境与装备技术协调创新中心, 南京 210044
  • 收稿日期:2021-12-10 修回日期:2022-02-21 发布日期:2022-08-31
  • 基金资助:
    国家自然科学基金(61973169)协同动态量化与事件驱动方法的滑模控制系统分析与设计,江苏省自然科学基金(BK20201392)资助课题.

李惠, 郑柏超, 吴跃文. Delta算子框架下混沌系统的自适应滑模控制[J]. 系统科学与数学, 2022, 42(7): 1685-1699.

LI Hui, ZHENG Bochao, WU Yuewen. Adaptive Sliding Mode Control of Chaotic Systems in Delta Operator Framework[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(7): 1685-1699.

Adaptive Sliding Mode Control of Chaotic Systems in Delta Operator Framework

LI Hui1, ZHENG Bochao1,2, WU Yuewen1   

  1. 1. School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044;
    2. Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing 210044
  • Received:2021-12-10 Revised:2022-02-21 Published:2022-08-31
针对DoS攻击和网络故障下的非线性耦合混沌系统,提出了一种Delta算子框架下自适应滑模控制方法.首先,对连续时间和离散时间的非线性耦合混沌系统,依据Delta算子理论,建立Delta算子框架下的统一模型.其次,对提出的Delta算子框架下的非线性混沌系统设计线性滑模面,并利用线性矩阵不等式方法给出滑模面存在的充分条件.再次,对上述系统提出自适应滑模控制器的设计方法,使之能够快速到达滑模面,实现在DoS攻击和网络故障下的非线性耦合混沌系统的鲁棒镇定.最后,仿真算例结果表明在所设计的自适应滑模控制器下,非线性耦合混沌系统状态稳定,并渐近趋向于零,说明了所提方法的可行性和有效性.
An adaptive sliding mode control method based on Delta operator is proposed for nonlinear chaotic systems under DoS attack and network failure. First, based on the Delta operator theory, a unified model under the Delta operator framework is established for continuous time and discrete time nonlinear chaotic systems.Second, the linear sliding surface is designed for the nonlinear chaotic system in the framework of Delta operator, and the sufficient conditions for the existence of the sliding surface are given by using the linear matrix inequality method. Third, adaptive sliding mode controller of the design method is proposed to the above system, which can ensure the reach ability of the method, and realize the stability of nonlinear chaotic system under DoS attack and network failure. Finally, the simulation results show that the system is stable and its states asymptotically tend to zero under the adaptive sliding mode controller, which shows the effectiveness of the proposed method.

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