Open Access
| Issue |
ESAIM: COCV
Volume 32, 2026
|
|
|---|---|---|
| Article Number | 13 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2025099 | |
| Published online | 25 February 2026 | |
- U. Serres, Geometry and Feedback Classification of Low-Dimensional Non-Linear Control Systems. PhD thesis, Université de Bourgogne (2006). [Google Scholar]
- M. Fliess, J. Levine, P. Martin and P. Rouchon, A Lie-Backlund approach to equivalence and flatness of nonlinear systems. IEEE Trans. Automatic Control 44 (1999) 922–937. [Google Scholar]
- A.A. Agrachev and R.V. Gamkrelidze, Feedback-invariant optimal control theory and differential geometry—I. Regular extremals. J. Dyn. Control Systems 3 (1997) 343–389. [CrossRef] [Google Scholar]
- U. Serres, On curvature and feedback classification of two-dimensional optimal control systems. J. Math. Sci. 144 (2007) 3841–3847. [Google Scholar]
- B. Jakubczyk, Equivalence and invariants of nonlinear control systems, in Nonlinear Controllability and Optimal Control, vol. 133, edited by H.J. Sussmann, editor. Marcel Dekker, New York (1990) 177–218. [Google Scholar]
- T. Schmoderer, Study of Control Systems under Quadratic Nonholonomic Constraints. Motion Planning, Introduction to the Regularised Continuation Method. PhD thesis, INSA Rouen Normandie (2022). [Google Scholar]
- T. Schmoderer and W. Respondek, Conic nonholonomic constraints on surfaces and control systems. J. Dyn. Control Syst. 29 (2023) 1981–2022. [Google Scholar]
- L.E. Dubins, On Curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79 (1957) 497. [Google Scholar]
- U. Serres, Control systems of zero curvature are not necessarily trivializable. arXiv:0902.2332 [math] (2009). [Google Scholar]
- A.A. Agrachev, Feedback-invariant optimal control theory and differentiaL geometry, II. Jacobi curves for singular extremals. J. Dyn. Control Syst. 4 (1998) 583–604. [CrossRef] [Google Scholar]
- G.R. Wilkens, Centro-affine geometry in the plane and feedback invariants of two-state scalar control systems, in Proceedings of Symposia in Pure Mathematics, vol. 64, edited by G. Ferreyra, R. Gardner, H. Hermes and H. Sussmann. American Mathematical Society, Providence, Rhode Island (1998) 319–333. [Google Scholar]
- A. Isidori, Nonlinear Control Systems. Communications and Control Engineering, Nonlinear Control Systems, 3rd edn. Springer-Verlag, London (1995). [Google Scholar]
- J. Grizzle and S. Marcus, The structure of nonlinear control systems possessing symmetries. IEEE Trans. Automatic Control 30 (1985) 248–258. [Google Scholar]
- W. Respondek and I.A. Tall, Nonlinearizable single-input control systems do not admit stationary symmetries. Syst. Control Lett. 46 (2002) 1–16. [Google Scholar]
- D. Burde and M. Ceballos, Abelian ideals of maximal dimension for solvable Lie algebras J. Lie Theory 22 (2012) 741–756. [Google Scholar]
- Z. Avetisyan, The structure of almost Abelian Lie algebras. Int. J. Math. 33 (2022) 2250057. [Google Scholar]
- W. Magnus, On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math. 7 (1954) 649–673. [Google Scholar]
- V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edn. Grundlehren der mathematischen Wissenschaften. Springer (1988). [Google Scholar]
- T. Schmoderer and W. Respondek, Null-forms of conic systems in ℝ3 are determined by their symmetries. Syst. Control Lett. 170 (2022) 105397. [Google Scholar]
- W. Respondek, Symmetries and minimal flat outputs of nonlinear control systems, in New Trends in Nonlinear Dynamics and Control and their Applications. Springer (2004) 65–86. [Google Scholar]
- A.A. Agrachev and Y. Sachkov, Control Theory from the Geometric Viewpoint, vol. 87. Springer Science & Business Media (2013). [Google Scholar]
- W. Respondek and S. Ricardo. Equivariants of mechanical control systems. SIAM J. Control Optim. 51 (2013) 3027–3055. [Google Scholar]
- B. Jakubczyk and W. Kryński, Vector fields with distributions and invariants of ODEs. J. Geom. Mech. 5 (2013) 85–129. [CrossRef] [MathSciNet] [Google Scholar]
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