The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems
- Author
- Marta Farré Puiggalí and Tom Mestdag (UGent)
- Organization
- Abstract
- We apply methods of the so-called "inverse problem of the calculus of variations" to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the inverted pendulum on a cart and the inertia wheel pendulum. By making use of a condition that follows from Douglas' classification, we derive feedback controls for which the control system is variational. We then use the energy of a suitable controlled Lagrangian to provide a stability criterion for the equilibrium.
- Keywords
- GENERALIZED HELMHOLTZ CONDITIONS, DIFFERENTIAL-EQUATIONS, controlled Lagrangians, inverse problem, stability, Lyapunov function
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8508869
- MLA
- Farré Puiggalí, Marta, and Tom Mestdag. “The Inverse Problem of the Calculus of Variations and the Stabilization of Controlled Lagrangian Systems.” SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 54, no. 6, 2016, pp. 3297–318, doi:10.1137/16M1060091.
- APA
- Farré Puiggalí, M., & Mestdag, T. (2016). The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 54(6), 3297–3318. https://doi.org/10.1137/16M1060091
- Chicago author-date
- Farré Puiggalí, Marta, and Tom Mestdag. 2016. “The Inverse Problem of the Calculus of Variations and the Stabilization of Controlled Lagrangian Systems.” SIAM JOURNAL ON CONTROL AND OPTIMIZATION 54 (6): 3297–3318. https://doi.org/10.1137/16M1060091.
- Chicago author-date (all authors)
- Farré Puiggalí, Marta, and Tom Mestdag. 2016. “The Inverse Problem of the Calculus of Variations and the Stabilization of Controlled Lagrangian Systems.” SIAM JOURNAL ON CONTROL AND OPTIMIZATION 54 (6): 3297–3318. doi:10.1137/16M1060091.
- Vancouver
- 1.Farré Puiggalí M, Mestdag T. The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems. SIAM JOURNAL ON CONTROL AND OPTIMIZATION. 2016;54(6):3297–318.
- IEEE
- [1]M. Farré Puiggalí and T. Mestdag, “The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems,” SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 54, no. 6, pp. 3297–3318, 2016.
@article{8508869,
abstract = {{We apply methods of the so-called "inverse problem of the calculus of variations" to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the inverted pendulum on a cart and the inertia wheel pendulum. By making use of a condition that follows from Douglas' classification, we derive feedback controls for which the control system is variational. We then use the energy of a suitable controlled Lagrangian to provide a stability criterion for the equilibrium.}},
author = {{Farré Puiggalí, Marta and Mestdag, Tom}},
issn = {{0363-0129}},
journal = {{SIAM JOURNAL ON CONTROL AND OPTIMIZATION}},
keywords = {{GENERALIZED HELMHOLTZ CONDITIONS,DIFFERENTIAL-EQUATIONS,controlled Lagrangians,inverse problem,stability,Lyapunov function}},
language = {{eng}},
number = {{6}},
pages = {{3297--3318}},
title = {{The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems}},
url = {{http://doi.org/10.1137/16M1060091}},
volume = {{54}},
year = {{2016}},
}
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