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Control Lyapunov functions and hybrid zero dynamics

Ames, Aaron D. and Galloway, Kevin and Grizzle, J. W. (2012) Control Lyapunov functions and hybrid zero dynamics. In: 51st IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 6837-6842. ISBN 978-1-4673-2066-5. https://resolver.caltech.edu/CaltechAUTHORS:20190213-085922450

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Abstract

Hybrid zero dynamics extends the Byrnes-Isidori notion of zero dynamics to a class of hybrid models called systems with impulse effects. Specifically, given a smooth submanifold that is contained in the zero set of an output function and is invariant under both the continuous flow of the system with impulse effects as well as its reset map, the restriction dynamics is called the hybrid zero dynamics. Prior results on the stabilization of periodic orbits of the hybrid zero dynamics have relied on input-output linearization of the transverse variables. The principal result of this paper shows how control Lyapunov functions can be used to exponentially stabilize periodic orbits of the hybrid zero dynamics, thereby significantly extending the class of stabilizing controllers. An illustration of this result on a model of a bipedal walking robot is provided.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC.2012.6426229DOIArticle
ORCID:
AuthorORCID
Ames, Aaron D.0000-0003-0848-3177
Grizzle, J. W.0000-0001-7586-0142
Additional Information:© 2012 IEEE. The work of A. D. Ames is supported by NSF grants CNS-0953823 and CNS-1136104, NHARP project 000512-0184-2009 and NASA contract NNX12AB58G, K. Galloway is supported by DARPA Contract W91CRB-11-1-0002, and J. Grizzle is supported in part by DARPA and by NSF grant ECS-909300.
Funders:
Funding AgencyGrant Number
NSFCNS-0953823
NSFCNS-1136104
Norman Hackerman Advanced Research Program (NHARP)000512-0184-2009
NASANNX12AB58G
Defense Advanced Research Projects Agency (DARPA)W91CRB-11-1-0002
NSFECS-909300
Record Number:CaltechAUTHORS:20190213-085922450
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190213-085922450
Official Citation:A. D. Ames, K. Galloway and J. W. Grizzle, "Control lyapunov functions and hybrid zero dynamics," 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, HI, 2012, pp. 6837-6842. doi: 10.1109/CDC.2012.6426229
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92874
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Feb 2019 18:27
Last Modified:15 Nov 2019 18:33

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