基于LMI的分段线性系统共存吸引子转迁控制研究

李得洋1,2,吴少培2,李国芳2,丁旺才2,丁杰2,俞力洋2,卫晓娟3

振动与冲击 ›› 2023, Vol. 42 ›› Issue (19) : 30-39.

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (19) : 30-39.
论文

基于LMI的分段线性系统共存吸引子转迁控制研究

  • 李得洋1,2,吴少培2,李国芳2,丁旺才2,丁杰2,俞力洋2,卫晓娟3
作者信息 +

LMI-based transfer control for coexisting attractors in piecewise linear system

  • LI Deyang1,2, WU Shaopei2, LI Guofang2, DING Wangcai2, DING Jie2, YU Liyang2, WEI Xiaojuan3
Author information +
文章历史 +

摘要

以一类两自由度含间隙分段线性系统为研究对象,利用线性矩阵不等式(LMI)和线性反馈方法对系统共存的吸引子进行在预期目标轨道引导下的转迁控制。首先,在状态平面上利用胞映射方法对系统随参数变化时的共存吸引子进行识别,并基于Poincaré映射和Lyapunov指数研究了系统共存吸引子的稳定性及转迁机理。其次,基于线性矩阵不等式(LMI)和Lyapunov理论,并利用系统的向量场信息和S-procedure,将系统施加线性反馈控制器后的稳定性和反馈增益矩阵的求解问题转化为LMI描述。最后利用数值方法验证了本文所应用的线性反馈控制器及其增益矩阵选取方法的可行性及正确性。

Abstract

The linear matrix inequality (LMI) and linear feedback method are used to migration the attractor under the guidance of the desired target orbit in a class of a two-degree-of-freedom piecewise-linearity system with clearance. Firstly, the coexisting attractors are identified on the state plane by cell mapping method. Meanwhile, the stability and transition mechanism of the coexisting attractors are studied based on Poincaré mapping and Lyapunov exponent. Secondly, according to the linear matrix inequality and Lyapunov theory, the stability of linear feedback control and the solution for feedback gain matrix are transformed into LMI description via the vector field information and s-procedure. Finally, the linear feedback controller and its gain matrix selection method are validated by numerical simulation.

关键词

分段线性系统 / 共存吸引子 / 线性矩阵不等式 / 吸引子转迁控制

Key words

Piecewise-linearity System / coexistent attractor / The linear matrix inequality / Attractor migration control

引用本文

导出引用
李得洋1,2,吴少培2,李国芳2,丁旺才2,丁杰2,俞力洋2,卫晓娟3. 基于LMI的分段线性系统共存吸引子转迁控制研究[J]. 振动与冲击, 2023, 42(19): 30-39
LI Deyang1,2, WU Shaopei2, LI Guofang2, DING Wangcai2, DING Jie2, YU Liyang2, WEI Xiaojuan3. LMI-based transfer control for coexisting attractors in piecewise linear system[J]. Journal of Vibration and Shock, 2023, 42(19): 30-39

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