TY - GEN
T1 - A route to limit cycles via unfolding the pitchfork with feedback
AU - Reverdy, Paul B.
N1 - Publisher Copyright:
© 2019 American Automatic Control Council.
PY - 2019/7
Y1 - 2019/7
N2 - 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.
AB - 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.
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U2 - 10.23919/acc.2019.8814843
DO - 10.23919/acc.2019.8814843
M3 - Conference contribution
AN - SCOPUS:85072292430
T3 - Proceedings of the American Control Conference
SP - 3057
EP - 3062
BT - 2019 American Control Conference, ACC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 American Control Conference, ACC 2019
Y2 - 10 July 2019 through 12 July 2019
ER -