The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Invertibility of Nonlinear Control Systems
Abstract
This paper gives necessary and sufficient conditions for the invertibility of nonlinear control systems of the form $\dot x = A(x) + uB(x)$; $y = c(x)$, where the state space is a real analytic manifold. For invertible systems we construct nonlinear inverse systems. These results are used to study the question of functional controllability for nonlinear systems. The class of real analytic functions which can appear as outputs of a given nonlinear system is described, and a prefilter is constructed to generate the required control.
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Citations
Cites
Nonlinear controllability and observability
Hermann, R., & Krener, A. (1977) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1977.1101601 · Cited by 2,374
Lie Groups, Lie Algebras, and Their Representations
Varadarajan, V. S. (1984) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-1126-6 · Cited by 1,739
Inversion of multivariable linear systems
Silverman, L. (1969) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1969.1099169 · Cited by 813
Controllability of nonlinear systems
Sussmann, H. J., & Jurdjevic, V. (1972) · Journal of Differential Equations · doi:10.1016/0022-0396(72)90007-1 · Cited by 805
Jurdjevic, V., & Sussmann, H. J. (1972) · Journal of Differential Equations · doi:10.1016/0022-0396(72)90035-6 · Cited by 630
Foundations of Differentiable Manifolds and Lie Groups.
Allendoerfer, C. B., & Warner, F. W. (1972) · The American Mathematical Monthly · doi:10.2307/2316291 · Cited by 600
Invertibility of linear time-invariant dynamical systems
Sain, M., & Massey, J. (1969) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1969.1099133 · Cited by 511
System Theory on Group Manifolds and Coset Spaces
Brockett, R. W. (1972) · SIAM Journal on Control · doi:10.1137/0310021 · Cited by 455
Volterra series and geometric control theory
Brockett, R. W. (1976) · Automatica · doi:10.1016/0005-1098(76)90080-7 · Cited by 366
Contrôlabilité des Systèmes non Linéaires
Lobry, C. (1970) · SIAM Journal on Control · doi:10.1137/0308042 · Cited by 243
Metadata
- Authors
- Hirschorn, R. M.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 1979-03
- Volume
- 17
- Issue
- 2
- Pages
- 289-297
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2046935643
- Cited by
- 288
- References
- 12
- FWCI
- 13.78
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hirschorn, R. M. (1979). Invertibility of Nonlinear Control Systems. SIAM Journal on Control and Optimization. https://doi.org/10.1137/0317022
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.
