The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics
Open accessAbstract
This paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models-systems with impulse effects-through control Lyapunov functions. The periodic orbit is assumed to lie in a C1submanifold Z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics; the associated restriction dynamics are termed the hybrid zero dynamics. The orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics. Prior results on the stabilization of such periodic orbits with respect to the full-order dynamics of the system with impulse effects have relied on input-output linearization of the dynamics transverse to the zero dynamics manifold. The principal result of this paper demonstrates that a variant of control Lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface, Z, can be used to achieve exponential stability of the periodic orbit in the full-order dynamics, thereby significantly extending the class of stabilizing controllers. The main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control Lyapunov functions.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Nonlinear and adaptive control design
Krstić, M., Kokotović, P. V., & Kanellakopoulos, I. (1995) · Cited by 10,421
Isidori, A. (1989) · Springer eBooks · doi:10.1007/978-3-662-02581-9 · Cited by 7,869
Isidori, A. (1995) · Communications and Control Engineering · doi:10.1007/978-1-84628-615-5 · Cited by 6,755
(2012) · SpringerReference · doi:10.1007/springerreference_117570 · Cited by 4,486
Constructive Nonlinear Control
Sepulchre, R., Janković, M., & Kokotović, P. V. (1997) · Communications and Control Engineering · doi:10.1007/978-1-4471-0967-9 · Cited by 2,297
Vidyasagar, M., & Desoer, C. A. (1980) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/tsmc.1980.4308549 · Cited by 2,011
Nonlinear Control Systems: An Introduction
(1985) · Lecture Notes in Control and Information Sciences · doi:10.1007/bfb0006368 · Cited by 1,852
On characterizations of the input-to-state stability property
Sontag, E. D., & Wang, Y. (1995) · Systems & Control Letters · doi:10.1016/0167-6911(94)00050-6 · Cited by 1,784
Sastry, S. (1999) · Interdisciplinary Applied Mathematics · doi:10.1007/978-1-4757-3108-8 · Cited by 1,764
Continuous finite-time stabilization of the translational and rotational double integrators
Bhat, S. P., & Bernstein, D. S. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.668834 · Cited by 1,694
Cited by
Xu, X., Tabuada, P., Grizzle, J. W., & Ames, A. D. (2015) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2015.11.152 · Cited by 586
Self-citationModels, feedback control, and open problems of 3D bipedal robotic walking
Grizzle, J. W., Chevallereau, C., Sinnet, R. W., & Ames, A. D. (2014) · Automatica · doi:10.1016/j.automatica.2014.04.021 · Cited by 321
Self-citationDawson, C., Gao, S., & Fan, C. (2023) · IEEE Transactions on Robotics · doi:10.1109/tro.2022.3232542 · Cited by 269
A review of current state-of-the-art control methods for lower-limb powered prostheses
Gehlhar, R., Tucker, M., Young, A. J., & Ames, A. D. (2023) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2023.03.003 · Cited by 131
Self-citationOnline Learning of Unknown Dynamics for Model-Based Controllers in Legged Locomotion
Sun, Y., Ubellacker, W. L., Ma, W.-L., Zhang, X., Wang, C., Csomay-Shanklin, N. V., Tomizuka, M., Sreenath, K., & Ames, A. D. (2021) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2021.3108510 · Cited by 54
Self-citation
Metadata
- Authors
- Ames, A. D., Galloway, K., Sreenath, K., & Grizzle, J. W.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2014-04
- Volume
- 59
- Issue
- 4
- Pages
- 876-891
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2171879251
- Cited by
- 440
- References
- 39
- FWCI
- 15.06
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics. https://app.cochat.ai/papers/10.1109/tac.2014.2299335
- The paper
- Ames, A. D., Galloway, K., Sreenath, K., & Grizzle, J. W. (2014). Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2014.2299335
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
