A structurally flat triangular form based on the extended chained form

References

• Bououden, S., Boutat, D., Zheng, G., Barbot, J., & Kratz, F. (2011). A triangular canonical form for a class of 0-flat nonlinear systems. International Journal of Control, 84(2), 261–269. https://doi.org/https://doi.org/10.1080/00207179.2010.549844
   Web of Science ®Google Scholar
• Cartan, E. (1914). Sur l'équivalence absolue de certains systèmes d'équations différentielles et sur certaines familles de courbes. Bulletin de la Société Mathématique de France, 42, 12–48.
   Google Scholar
• Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1992). Sur les systèmes non linéaires différentiellement plats. Comptes Rendus de l'Académie des Sciences. Série I, Mathématique, 315, 619–624.
   Google Scholar
• Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1995). Flatness and defect of non-linear systems: Introductory theory and examples. International Journal of Control, 61(6), 1327–1361. https://doi.org/https://doi.org/10.1080/00207179508921959
   Web of Science ®Google Scholar
• Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1999). A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922–937. https://doi.org/https://doi.org/10.1109/9.763209
   Web of Science ®Google Scholar
• Gstöttner, C., Kolar, B., & Schöberl, M. (2020). On a flat triangular form based on the extended chained form. arXiv:2002.01203 [math.DS], accepted for MTNS 2020 (conference postponed to 2021).
   Google Scholar
• Hunt, L., & Su, R. (1981). Linear equivalents of nonlinear time varying systems. In Proceedings 5th international symposium on mathematical theory of networks and systems (MTNS) (pp. 119–123).
   Google Scholar
• Jakubczyk, B., & Respondek, W. (1980). On linearization of control systems. Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, 28, 517–522.
   Google Scholar
• Kolar, B., Schöberl, M., & Schlacher, K. (2015). Remarks on a Triangular Form for 1-Flat Pfaffian Systems with Two Inputs. In Proceedings 1st IFAC conference on modelling, identification and control of nonlinear systems (micnon). (IFAC-PapersOnLine, Vol. 48(11), pp. 109–114).
   Google Scholar
• Lévine, J. (2009). Analysis and control of nonlinear systems: A flatness-based approach. Springer.
   Google Scholar
• Li, S., Nicolau, F., & Respondek, W. (2016). Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness. International Journal of Control, 89(1), 1–24. https://doi.org/https://doi.org/10.1080/00207179.2015.1056232
   Web of Science ®Google Scholar
• Li, S., & Respondek, W. (2012). Flat outputs of two-input driftless control systems. ESAIM: Control, Optimisation and Calculus of Variations, 18(3), 774–798. https://doi.org/https://doi.org/10.1051/cocv/2011181
   Web of Science ®Google Scholar
• Li, S., Xu, C., Su, H., & Chu, J. (2013). Characterization and flatness of the extended chained system. In Proceedings of the 32nd Chinese control conference (pp. 1047–1051).
   Google Scholar
• Martin, P., Devasia, S., & Paden, B. (1996). A different look at output tracking: Control of a VTOL aircraft. Automatica, 32(1), 101–107. https://doi.org/https://doi.org/10.1016/0005-1098(95)00099-2
   Web of Science ®Google Scholar
• Martin, P., & Rouchon, P. (1994). Feedback linearization and driftless systems. Mathematics of Control, Signals, and Systems, 7(3), 235–254. https://doi.org/https://doi.org/10.1007/BF01212271
   Web of Science ®Google Scholar
• Murray, R. (1994). Nilpotent bases for a class of non-integrable distributions with applications to trajectory generation for nonholonomic systems. Mathematics of Control, Signals, and Systems, 7(1), 58–75. https://doi.org/https://doi.org/10.1007/BF01211485
   Web of Science ®Google Scholar
• Nicolau, F. (2014). Geometry and flatness of control systems of minimal differential weight [Theses]. INSA de Rouen.
   Google Scholar
• Nicolau, F., Li, S., & Respondek, W. (2014). Control-affine systems compatible with the multi-chained form and their x-maximal flatness. In Proceedings 21st international symposium on mathematical theory of networks and systems (MTNS) (pp. 303–310).
   Google Scholar
• Nicolau, F., & Respondek, W. (2016a, December). Flatness of two-input control-affine systems linearizable via a two-fold prolongation. In 2016 IEEE 55th conference on decision and control (CDC) (pp. 3862–3867).
   Google Scholar
• Nicolau, F., & Respondek, W. (2016b). Two-input control-affine systems linearizable via one-fold prolongation and their flatness. European Journal of Control, 28, 20–37. https://doi.org/https://doi.org/10.1016/j.ejcon.2015.11.001
   Web of Science ®Google Scholar
• Nicolau, F., & Respondek, W. (2017). Flatness of multi-input control-affine systems linearizable via one-fold prolongation. SIAM Journal Control and Optimization, 55(5), 3171–3203. https://doi.org/https://doi.org/10.1137/140999463
   Web of Science ®Google Scholar
• Nicolau, F., & Respondek, W. (2019). Normal forms for multi-input flat systems of minimal differential weight. International Journal of Robust and Nonlinear Control, 29(10), 3139–3162. https://doi.org/https://doi.org/10.1002/rnc.v29.10
   Web of Science ®Google Scholar
• Nicolau, F., & Respondek, W. (2020). Normal forms for flat two-input control systems linearizable via a two-fold prolongation. In Proceedings 21st IFAC world congress.
   Google Scholar
• Nijmeijer, H., & van der Schaft, A. (1990). Nonlinear dynamical control systems. Springer.
   Google Scholar
• Pomet, J. (1997). On dynamic feedback linearization of four-dimensional affine control systems with two inputs. ESAIM: Control, Optimisation and Calculus of Variations, 2, 151–230. https://doi.org/https://doi.org/10.1051/cocv:1997107
   Google Scholar
• Schlacher, K., & Schöberl, M. (2013). A jet space approach to check Pfaffian systems for flatness. In Proceedings 52nd IEEE conference on decision and control (CDC) (pp. 2576–2581).
   Google Scholar
• Schöberl, M. (2014). Contributions to the analysis of structural properties of dynamical systems in control and systems theory – a geometric approach. Shaker Verlag.
   Google Scholar
• Schöberl, M., Rieger, K., & Schlacher, K. (2010). System parametrization using affine derivative systems. In Proceedings 19th international symposium on mathematical theory of networks and systems (MTNS) (pp. 1737–1743).
   Google Scholar
• Schöberl, M., & Schlacher, K. (2011). On calculating flat outputs for Pfaffian systems by a reduction procedure – demonstrated by means of the VTOL example. In 9th IEEE international conference on control & automation (ICCA11) (pp. 477–482).
   Google Scholar
• Schöberl, M., & Schlacher, K. (2014). On an implicit triangular decomposition of nonlinear control systems that are 1-flat – a constructive approach. Automatica, 50(6), 1649–1655. https://doi.org/https://doi.org/10.1016/j.automatica.2014.04.007
   Web of Science ®Google Scholar
• Silveira, H., Pereira, P., & Rouchon, P. (2015). A flat triangular form for nonlinear systems with two inputs: necessary and sufficient conditions. European Journal of Control, 22, 17–22. https://doi.org/https://doi.org/10.1016/j.ejcon.2015.01.001
   Web of Science ®Google Scholar