A route to limit cycles via unfolding the pitchfork with feedback
A route to limit cycles via unfolding the pitchfork with feedback
复制标题
通过利用反馈展开干草叉来限制循环的路线
DOI：
10.23919/acc.2019.8814843
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Paul B. Reverdy
中科院分区：
文献类型：
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作者：
Paul B. Reverdy
基于开发一个能够在低阶控制向量场之间切换的系统的问题，我们研究了一个基于干草叉分叉的决策机制与一个由两个控制向量场线性组合给出动力学的对象之间的反馈互连；干草叉系统的状态决定了植物的线性组合系数。我们展示了如何使用控制向量场的Lyapunov函数作为干草叉中的展开参数将植物状态反馈到干草叉，并推导了闭环系统表现出导致稳定极限环的Hopf分岔的条件。
Motivated by the problem of developing a system that can switch between low-level control vector fields, we study the feedback interconnection of a decision mechanism based on the pitchfork bifurcation with a plant whose dynamics are given by the linear combination of two control vector fields; the state of the pitchfork system then determines the linear combination coefficients for the plant. We show how the plant state can be fed back to the pitchfork by using the Lyapunov functions of the control vector fields as an unfolding parameter in the pitchfork, and derive conditions under which the closed-loop system exhibits a Hopf bifurcation leading to stable limit cycles.
影响因子：
4.2
作者：
Gray, Rebecca;Franci, Alessio;Leonard, Naomi Ehrich
通讯作者：
Leonard, Naomi Ehrich