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A General Theorem on Local Controllability
Abstract
We prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point. Earlier results of Brunovsky, Hermes, Jurdjevic, Crouch and Byrnes, Sussmann and Grossmann, are shown to be particular cases of this result. Also, a number of new sufficient conditions are obtained. All these results follow from one simple general principle, namely, that local controllability follows whenever brackets with certain symmetries can be “neutralized,” in a suitable way, by writing them as linear combinations of brackets of a lower degree. Both the class of symmetries and the definition of “degree” can be chosen to suit the problem.
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Cited by
Dynamics and control of a class of underactuated mechanical systems
Reyhanoglu, M., van der Schaft, A., Mcclamroch, N. H., & Kolmanovsky, I. (1999) · IEEE Transactions on Automatic Control · doi:10.1109/9.788533 · Cited by 501
Stable Pushing: Mechanics, Controllability, and Planning
Lynch, K. M., & Mason, M. T. (1996) · The International Journal of Robotics Research · doi:10.1177/027836499601500602 · Cited by 463
Spong (1998) · doi:10.1007/bfb0015081 · Cited by 437
Metadata
- Authors
- Sussmann, H. J.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 1987-01
- Volume
- 25
- Issue
- 1
- Pages
- 158-194
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W1985578018
- Cited by
- 634
- References
- 0
- FWCI
- 12.47
- Type
- journal article
- Language
- en
- Open access
- closed
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- Sussmann, H. J. (1987). A General Theorem on Local Controllability. SIAM Journal on Control and Optimization. https://doi.org/10.1137/0325011
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