On necessary and sufficient conditions for differential flatness
Tóm tắt
Từ khóa
Tài liệu tham khảo
Anderson R.L., Ibragimov N.H. (1979) Lie-Bäcklund Transformations in Applications. SIAM, Philadelphia
Antritter, F., Lévine, J.: Towards a computer algebraic algorithm for flat output determination. In: Proceedings of ISSAC’08, Hagenberg, Austria (2008)
Aranda-Bricaire E., Moog C.H., Pomet J.-B. (1995) A linear algebraic framework for dynamic feedback linearization. IEEE Trans. Automat. Contr. 40(1): 127–132
Avanessoff D., Pomet J.-B. (2007) Flatness and monge parameterization of two-input systems, control-affine with 4 states or general with 3 states. ESAIM. Contrôle, optimisation et calcul des variations 13(2): 237–264
Bers, L.: On Hilbert’s 22nd problem. In: Browder, F. (ed.) Mathematical Developments Arising From Hilbert Problems, Proceedings of Symposia in Pure Mathematics, pp. 559–609. American Mathematical Society, Providence, Rhode Island (1976)
Bryant R.L., Chern S.S., Gardner R.B., Goldschmitt H.L., Griffiths P.A. (1991) Exterior Differential Systems, vol. 18 of Mathematical Sciences Research Institute Publications. Springer, Berlin
Cartan, É.: Sur l’équivalence absolue de certains systèmes d’équations différentielles et sur certaines familles de courbes. Bull. Soc. Math. Fr. 42, 12–48 (1914). In Oeuvres Complètes, part II, vol 2, pp. 1133–1168, CNRS, Paris, 1984
Charlet B., Lévine J., Marino R. (1989) On dynamic feedback linearization. Syst. Control Lett. 13: 143–151
Charlet B., Lévine J., Marino R. (1991) Sufficient conditions for dynamic state feedback linearization. SIAM J. Control Optim. 29(1): 38–57
Chern S.S., Chen W.H., Lam K.S. (2000) Lectures on Differential Geometry, vol. 1 of Series on University Mathematics. World Scientific, Singapore
Chetverikov, V.N.: New flatness conditions for control systems. In: Proceedings of NOLCOS’01, St. Petersburg, pp. 168–173 (2001)
Chetverikov, V.N.: Flatness conditions for control systems. Preprint DIPS (2002). Available via internet. http://www.diffiety.ac.ru
Chyzak F., Quadrat A., Robertz D. (2005) Effective algorithms for parametrizing linear control systems over Ore algebras. Appl. Algebra Eng. Commun. Comput. 16(5): 319–376
Cohn P.M. (1985) Free Rings and Their Relations. Academic Press, London
Fliess M. (1990) Some basic structural properties of generalized linear systems. Syst. Control Lett. 15: 391–396
Fliess M. (1992) A remark on Willems’ trajectory characterization of linear controllability. Syst. Control Lett. 19: 43–45
Fliess M., Lévine J., Martin P.H., Ollivier F., Rouchon P. (1997) Controlling nonlinear systems by flatness. In: Byrnes C.I., Datta B.N., Gilliam D.S., Martin C.F. (eds) Systems and Control in the Twenty-First Century. Birkhäuser, Boston, pp 137–154
Fliess M., Lévine J., Martin P.H., Rouchon P. (1992) Sur les systèmes non linéaires différentiellement plats. C. R. Acad. Sci. Paris I–315: 619–624
Fliess M., Lévine J., Martin P.H., Rouchon P. (1995) Flatness and defect of nonlinear systems: introductory theory and examples. Int. J. Control 61(6): 1327–1361
Fliess M., Lévine J., Martin P.H., Rouchon P. (1999) A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Trans. Automat. Contr. 44(5): 922–937
Franch, J.: Flatness, Tangent Systems and Flat Outputs. PhD thesis, Universitat Politècnica de Catalunya Jordi Girona (1999)
Goursat E. (1905) Sur le problème de Monge. Bull. Soc. Math. t. 33: 201–210
Hadamard J. (1901) Sur l’équilibre de plaques élastiques circulaires libres ou appuyées et celui de la sphère isotrope. Ann. Éc. Norm. Sér. 3, t. 18: 313–342
Hilbert, D.: Mathematische probleme. Archiv für Mathematik und Physik 1, 44–63 and 213–237 (1901). Also in Gesammelte Abhandlungen, vol. 3, pp. 290–329, Chelsea, New York (1965)
Hilbert, D.: Über den Begriff der Klasse von Differentialgleichungen. Math. Ann. 73, 95–108 (1912). Also in Gesammelte Abhandlungen, vol. 3, pp. 81–93, Chelsea, New York (1965)
Hunt L.R., Su R., Meyer G. (1983) Design for multi-input nonlinear systems. In: Brockett R.W., Millman R.S., Sussmann H.J. (eds) Differential Geometric Control Theory. Birkhäuser, Boston, pp 268–298
Jakubczyk, B.: Invariants of dynamic feedback and free systems. In: Proceedings of the ECC’93, Groningen, pp. 1510–1513 (1993)
Jakubczyk B., Respondek W. (1980) On linearization of control systems. Bull. Acad. Pol. Sci. Ser. Sci. Math. 28(9–10): 517–522
Kondratieva, M.V., Mikhalev, A.V., Pankratiev, E.V.: On Jacobi’s bound for systems of differential polynomials, pp. 79–85. Algebra, Moscow University Press, Moscow (1982, in russian)
Kostrikin A.I., Shafarevich I.R., Shafarevich I.R. (1980) Algebra, I., vol. 11 of Encyclopaedia of Mathematical Sciences. Springer, New York
Krasil’shchik I.S., Lychagin V.V., Vinogradov A.M. (1986) Geometry of Jet Spaces and Nonlinear Partial Differential Equations. Gordon and Breach, New York
Lévine, J.: On necessary and sufficient conditions for differential flatness. In: Proceedings of IFAC NOLCOS 2004 Conference, Stuttgart (2004)
Lévine, J.: On necessary and sufficient conditions for differential flatness. http://www.arxiv.org , arXiv:math.OC/0605405 (2006)
Lévine J. (2009) Analysis and Control of Nonlinear Systems: A Flatness-based Approach. Mathematical Engineering. Springer, Berlin
Lévine J., Nguyen D.V. (2003) Flat output characterization for linear systems using polynomial matrices. Syst. Control Lett. 48: 69–75
Martin, P.H.: Contribution à l’Étude des Systèmes Diffèrentiellement Plats. PhD thesis, École des Mines de Paris (1992)
Martin, P.H., Murray, R.M., Rouchon, P.: Flat systems. In: Bastin, G., Gevers, M. (eds.) Plenary Lectures and Minicourses, Proceedings of the ECC 97, Brussels, pp. 211–264 (1997)
Martin, P.H., Rouchon, P.: Systems without drift and flatness. In: Proceedings MTNS 93, Regensburg, Germany, August (1993)
Monge, G.: Supplément où l’on fait savoir que les équations aux différences ordinaires, pour lesquelles les conditions d’intégrabilité ne sont pas satisfaites sont susceptibles d’une véritable intégration et que c’est de cette intégration que dépend celle des équations aux différences partielles élevées. Mémoires de l’Académie Royale des Sciences, pp. 502–576 (1787)
Ollivier, F.: Standard bases of differential ideals. In: Proceedings of AAECC8, vol. 508 of Lecture Notes In Computer Science, pp. 304–321. Springer, Berlin (1990)
Ollivier F., Brahim S. (2007) La borne de Jacobi pour une diffiété définie par un système quasi régulier (Jacobi’s bound for a diffiety defined by a quasi-regular system). C. R. Math. 345(3): 139–144
Pereira da Silva, P.S.: Flatness of nonlinear control systems: a Cartan-Kähler approach. In: Proceedings of the Mathematical Theory of Networks and Systems (MTNS’2000), Perpignan, pp. 1–10 (2000)
Pereira da Silva P.S., Corrêa Filho C. (2001) Relative flatness and flatness of implicit systems. SIAM J. Control Optim. 39(6): 1929–1951
Poincaré, H.: Sur l’uniformisation des fonctions analytiques. Acta Mathematica 31, 1–63 (1907). Also in Œuvres de Henri Poincaré, t. 4, pp. 70–139, Gauthier-Villars, Paris (1950)
Polderman J.W., Willems J.C. (1998) Introduction to Mathematical System Theory: A Behavioral Approach. Texts in Applied Mathematics, vol. 26. Springer, New York
Pomet J.-B. (1993) A differential geometric setting for dynamic equivalence and dynamic linearization. In: Jakubczyk B., Respondek W., Rzeżuchowski T. (eds) Geometry in Nonlinear Control and Differential Inclusions. Banach Center Publications, Warsaw, pp 319–339
Pomet, J.-B.: On dynamic feedback linearization of four-dimensional affine control systems with two inputs. ESAIM-COCV (1997). http://www.emath.fr/Maths/Cocv/Articles/articleEng.html
Pommaret J.F., Quadrat A. (1999) Localization and parametrization of linear multidimensional control systems. Syst. Control Lett. 37: 247–269
Rathinam M., Murray R.M. (1998) Configuration flatness of Lagrangian systems underactuated by one control. SIAM J. Control Optim. 36(1): 164–179
Ritt J.F. (1935) Jacobi’s problem on the order of a system of differential equations. Ann. Math. 36: 303–312
Rouchon P. (1994) Necessary condition and genericity of dynamic feedback linearization. J. Math. Syst. Estim. Control 4(2): 257–260
Rouchon, P., Fliess, M., Lévine, J., Martin, P.H.: Flatness and motion planning: the car with n-trailers. In: Proceedings of the ECC’93, Groningen, pp. 1518–1522 (1993)
Rouchon, P., Fliess, M., Lévine, J., Martin, P.H.: Flatness, motion planning and trailer systems. In: Proceedings of the IEEE Conference Decision and Control, San Antonio (1993)
Rudolph J. (2003) Flatness Based Control of Distributed Parameter Systems. Shaker Verlag, Aachen
Rudolph J., Winkler J., Woittenek F. (2003) Flatness Based Control of Distributed Parameter Systems: Examples and Computer Exercises from Various Technological Domains. Shaker Verlag, Aachen
Schlacher, K., Schöberl, M.: Construction of flat outputs by reduction and elimination. In: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, Pretoria, South Africa, pp. 666–671 (2007)
Serret, J.-A.: Sur l’intégration de l’équation dx 2 + dy 2 + dz 2 = ds 2. J. Math. pure et appl. 1ère série, t. 13, 353–368 (1848)
Shadwick W.F. (1990) Absolute equivalence and dynamic feedback linearization. Syst. Control Lett. 15: 35–39
Sluis W.M. (1993) A necessary condition for dynamic feedback linearization. Syst. Control Lett. 21: 277–283
Trentelman H.L. (1992) On flat systems behaviors and observable image representations. Syst. Control Lett. 19: 43–45
Van Nieuwstadt M., Rathinam M., Murray R.M. (1998) Differential flatness and absolute equivalence of nonlinear control systems. SIAM J. Control Optim. 36(4): 1225–1239
Yosida K. (1980) Functional Analysis, vol. 123 of Grundlehren der Mathematischen Wissenschaften, 6th edn. Springer, Berlin
Zervos P. (1913) Sur l’intégration de certains systèmes indéterminés d’équations différentielles. Journal für die reine und angewandte Mathematik 143: 300–312
Zervos P. (1932) Le problème de Monge. Mémorial des Sciences Mathématiques, fascicule LIII. Gauthier-Villars, Paris