Feedback linearization and driftless systems

R. Abraham, J. E. Marsden, and T. Ratiu,Manifolds, Tensor Analysis, and Applications, 2nd edn., Springer-Verlag, New York, 1988.

R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths,Exterior Differential Systems, Springer-Verlag, New York, 1991.

C. Caratheodory, Untersuchungen über die Grundlagen der Thermodynamik,Math. Ann.,67 (1909), 355?386.

E. Cartan, Sur l'équivalence absolue de certains systèmes d'équations différentielles et sur certaines familles de courves,Bull. Soc. Math. France,42 (1914), 12?48. Also inOeuvres Complètes, part II, vol. 2, CNRS, Paris, 1984, pp. 1133?1168.

E. Cartan, Sur l'intégration de certains systèmes indéterminés d'équations différentielles,J. Reine Angew. Math.,145 (1915), 86?91. Also inOeuvres Complètes, part II, vol. 2, CNRS, Paris, 1984, pp. 1164?1174.

B. Charlet, J. Lévine, and R. Marino, On dynamic feedback linearization,Systems Control Lett.,13 (1989), 143?151.

W. L. Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung,Math. Ann.,177 (1940), 98?105.

M. D. Di Benedetto, J. W. Grizzle, and C. H. Moog, Rank invariants of nonlinear systems,SIAM J. Control Optim.,27 (1989), 658?672.

M. Fliess, J. Lévine, Ph. Martin, and P. Rouchon, Sur les systèmes non linéaires différentiellement plats,C. R. Acad. Sci. Paris Sér. I,315 (1992), 619?624.

M. Fliess, J. Lévine, Ph. Martin, and P. Rouchon, Flatness and defect of nonlinear systems: introductory theory and examples,Internat. J. Control (1955), to appear.

M. Fliess, J. Lévine, Ph. Martin, and P. Rouchon, Towards a new differential geometric setting in nonlinear control,Proc. Internat. Geom. Colloq., Moscow, 1993 World Scientific, Singapore, to appear.

B. Gardner and W. F. Shadwick, Feedback equivalence for general control systems,Systems Control Lett,15 (1990), 15?23.

B. Gardner and W. F. Shadwick, Symmetry and the implementation of feedback linearization,Systems Control Lett.,15 (1990), 25?33.

B. Gardner and W. F. Shadwick, The GS algorithm for exact linearization to Brunovsky normal form,IEEE Trans. Automat. Control,37 (1992), 224?230.

A. Giaro, A. Kumpera, and C. Ruiz, Sur la lecture d'un résultat d'Élie Cartan,C. R. Acad. Sci. Paris Sér. A,287 (1978), 241?244.

R. Hermann, Some remarks on the geometry of systems, inGeometric Methods in Systems Theory (D. Q. Mayne and R. W. Brockett, eds.), Reidel, Dordrecht, 1973, pp. 237?242.

D. Hilbert, Über den Begriff der Klasse von Differentialgleichungen,Math. Ann. 73 (1912), 95?108. Also inGesammelte Abhandlungen, vol. III, Chelsea, New York, 1965, pp. 81?93.

L. R. Hunt, R. Su, and G. Meyer, Global transformations of nonlinear systems,IEEE Trans. Automat. Control,28 (1983), 24?31.

A. Isidori, Control of nonlinear systems via dynamic state feedback, inAlgebraic and Geometric Methods in Nonlinear Control Theory (M. Fliess and M. Hazewinkel, eds.), Reidel, Dordrecht, 1986.

A. Isidori, C. H. Moog, and A. De Luca, A sufficient condition for full linearization via dynamic state feedback,Proc. 25th IEEE Conf. Decision and Control, 1986, pp. 203?208.

B. Jakubczyk, Remarks on equivalence and linearization of nonlinear systems,Proc. IFAC Symp. NOLCOS '92, Bordeaux, 1992, pp. 393?397.

B. Jakubczyk, Invariants of dynamic feedback and free systems,Proc. ECC '93, Groningen, 1993, pp. 1510?1513.

B. Jakubczyk and W. Respondek, On linearization of control systems,Bull. Acad. Polon. Sci. Sér. Sci. Math.,28 (1980), 517?522.

A. Kumpera and C. Ruiz, Sur l'équivalence locale des systèmes de Pfaff en drapeau,Monge-Ampère Equations and Related Topics. Proc. Sem., Firenze, 1980 (F. Gherardelli, ed.), Inst. Naz. di Alta. Math., 1982, pp. 201?248.

J. P. Laumond and T. Siméon, Motion planning for a two degrees of freedom mobile with towing,Proc. IEEE Internat: Conf. Control and Applications, 1989.

Ph. Martin, Contribution à l'étude des systèmes diffèrentiellement plats, Ph.D. thesis, École des Mines de Paris, 1992.

Ph. Martin, Endogenous feedbacks and equivalence,Proc. MTNS 93, Regensburg, August 1993.

Ph. Martin and P. Rouchon, Systems without drift and flatness,Proc. MTNS 93, Regensburg, August 1993.

Ph. Martin and P. Rouchon, Any (controllable) driftless system with 3 inputs and 5 states is flat,Systems Control Lett., to appear.

R. M. Murray, Nilpotent Bases for a Class of Non-Integrable Distributions with Applications to Trajectory Generation for Nonholonomic Systems, Tech. Report CIT-CDS 92-002, Control and Dynamical Systems, California Institute of Technology, 1992.

R. M. Murray and S. S. Sastry, Nonholonomic motion planning: steering using sinusoids,IEEE Trans. Automat. Control,38 (1993), 700?716.

M. van Nieuwstadt, M. Rathinam, and R. M, Murráy, Differential Flatness and Absolute Equivalence, Tech. Report CIT-CDS 94-006, Control and Dynamical Systems, California Institute of Technology, March 1994.

J. B. Pomet, C. Moog, and E. Aranda, A non-exact Brunovsky form and dynamic feedback linearization,Proc. 31st IEEE Conf. Decision and Control, 1992, pp. 2012?2017.

P. K. Rashevsky, Any two points of a totally nonholonomic space may be connected by an admissible line,Uchen. Zap Ped. Inst. im. Liebknechta. Ser. Phys. Math.,2 (1938), 83?94 (in Russian).

P. Rouchon, Necessary condition and genericity of dynamic feedback linearization,J. Math. Systems Estim. Control,4(2) (1994).

P. Rouchon, M. Fliess, J. Lévine, and Ph. Martin, Flatness, motion planning and trailer systems,Proc. 32nd IEEE Conf. Decision and Control, San Antonio, December 1993, pp. 2700?2705.

W. F. Shadwick, Absolute equivalence and dynamic feedback linearization,Systems Control Lett.,15 (1990), 35?39.

W. M. Sluis, Absolute Equivalence and Its Application to Control Theory, Ph.D. thesis, University of Waterloo, Ontario, 1992.

D. Tilbury, R. Murray, and S. Sastry, Trajectory Generation for then-Trailer Problem Using Goursat Normal Form, Tech. Report UCB/ERL M93/12, Electronics Research Laboratory, University of California at Berkeley, February 1993.