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Energy shaping of hybrid systems via control Lyapunov functions

Sinnet, Ryan W. and Ames, Aaron D. (2015) Energy shaping of hybrid systems via control Lyapunov functions. In: 2015 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 5992-5997. ISBN 978-1-4799-8684-2.

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This paper presents a method for adding robustness to periodic orbits in hybrid dynamical systems by shaping the energy. This energy shaping method is similar to existing methods but improves upon them by utilizing control Lyapunov functions which allow for formal results on stability. The main theoretical result, Theorem 1, states that, given an exponentially-stable limit cycle in a hybrid dynamical system, application of the presented energy shaping controller results in a closed-loop system which is exponentially stable. As illustrated through simulation on the compass gait biped, this method turns out to be useful in practice, providing an improvement in robustness and convergence properties while maintaining existing stability.

Item Type:Book Section
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Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2015 AACC. This work was supported by NSF grant CNS-0953823.
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Record Number:CaltechAUTHORS:20190208-110812085
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Official Citation:R. W. Sinnet and A. D. Ames, "Energy shaping of hybrid systems via control Lyapunov functions," 2015 American Control Conference (ACC), Chicago, IL, 2015, pp. 5992-5997. doi: 10.1109/ACC.2015.7172280
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92793
Deposited By: Tony Diaz
Deposited On:08 Feb 2019 19:42
Last Modified:16 Nov 2021 03:53

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