Quelques résultats sur la commandabilité et la stabilisation des systèmes non linéaires

Coron, Jean-Michel

Journées mathématiques X-UPS, Aspects de la théorie du contrôle (1999), pp. 127-174.

[1] Bonnans, Frédéric; Rouchon, Pierre Analyse et commandes de systèmes dynamiques, Les Éditions de l’École Polytechnique, Palaiseau, 1998

[2] Bonnard, B. Contrôle de l’attitude d’un satellite rigide, RAIRO, Autom. Syst. Anal. Control, Volume 16 (1982), pp. 85-93 | Zbl

[3] Brockett, R. W. Asymptotic stability and feedback stabilization, Differential geometric control theory (Houghton, Mich., 1982) (Progress in Math.), Volume 27, Birkhäuser Boston, Boston, MA, 1983, pp. 181-191 | MR | Zbl

[4] Chow, W. L. Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann., Volume 117 (1940/1941), pp. 98-105 http://eudml.org/doc/160043 | DOI | Zbl

[5] Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. Asymptotic stability and smooth Lyapunov functions, J. Differential Equations, Volume 149 (1998) no. 1, pp. 69-114 | DOI | MR | Zbl

[6] Coron, Jean-Michel Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, Volume 5 (1992) no. 3, pp. 295-312 | DOI | MR | Zbl

[7] Coron, Jean-Michel On the stabilization of controllable and observable systems by an output feedback law, Math. Control Signals Systems, Volume 7 (1994) no. 3, pp. 187-216 | DOI | MR | Zbl

[8] Coron, Jean-Michel On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback law, SIAM J. Control Optim., Volume 33 (1995) no. 3, pp. 804-833 | DOI | MR | Zbl

[9] Coron, Jean-Michel On the controllability of $2$-D incompressible perfect fluids, J. Math. Pures Appl. (9), Volume 75 (1996) no. 2, pp. 155-188 | MR

[10] Coron, Jean-Michel On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions, ESAIM Contrôle Optim. Calc. Var., Volume 1 (1996), pp. 35-75 | DOI | Numdam | MR | Zbl

[11] Coron, Jean-Michel On the stabilization of some nonlinear control systems : results, tools, and applications, Nonlinear analysis, differential equations and control (Montreal, QC, 1998) (NATO Sci. Ser. C Math. Phys. Sci.), Volume 528, Kluwer Acad. Publ., Dordrecht, 1999, pp. 307-367 | DOI | MR | Zbl

[12] Coron, Jean-Michel; Keraï, El-Yazid Explicit feedbacks stabilizing the attitude of a rigid spacecraft with two control torques, Automatica J. IFAC, Volume 32 (1996) no. 5, pp. 669-677 | DOI | MR | Zbl

[13] Coron, Jean-Michel; Praly, Laurent; Teel, Andrew Feedback stabilization of nonlinear systems : sufficient conditions and Lyapunov and input-output techniques, Trends in control (Rome, 1995), Springer, Berlin, 1995, pp. 293-348 | DOI

[14] Crouch, Peter E. Spacecraft attitude control and stabilization : Applications of geometric control theory to rigid body models, IEEE Trans. Autom. Control, Volume 29 (1984), pp. 321-331 | DOI | Zbl

[15] Faurre, Pierre; Depeyrot, Michel Éléments d’automatique, 1, Dunod, Paris-Brussels-Montreal, Que., 1974

[16] Fliess, Michel; Lévine, Jean; Martin, Ph.; Rouchon, Pierre Flatness and defect of non-linear systems : introductory theory and examples, International Journal of Control, Volume 61 (1995) no. 6, pp. 1327-1361 | DOI | MR | Zbl

[17] Freeman, Randy A.; Kokotović, Petar V. Robust nonlinear control design. State-space and Lyapunov techniques, Modern Birkhäuser Classics, Birkhäuser, Boston, 2008

[18] Hahn, Wolfgang Stability of motion, Grundlehren Math. Wissen., 138, Springer-Verlag New York, Inc., New York, 1967 | DOI

[19] Hartman, Philip Ordinary differential equations, Classics in Applied Math., 38, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002 | DOI

[20] Hermann, Robert On the accessibility problem in control theory, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 325-332 | DOI | Zbl

[21] Horsin, T. On the controllability of the Burgers equation, ESAIM Contrôle Optim. Calc. Var., Volume 3 (1998), pp. 83-95 | DOI | MR | Zbl

[22] Isidori, Alberto Nonlinear control systems, Communications and Control Engineering Series, Springer-Verlag, Berlin, 1995 | DOI

[23] Kavian, Otared Introduction à la théorie des points critiques et applications aux problèmes elliptiques, Math. & Applications, 13, Springer-Verlag, Paris, 1993

[24] Kawski, Matthias Stabilization of nonlinear systems in the plane, Systems Control Lett., Volume 12 (1989) no. 2, pp. 169-175 | DOI | MR | Zbl

[25] Krasnosel’skiĭ, Mark Aleksandrovich The operator of translation along the trajectories of differential equations, Transl. Math. Monogr., 19, American Mathematical Society, Providence, RI, 1968 | DOI

[26] Krasnosel’skiĭ, Mark Aleksandrovich; Zabreiko, P. P. Geometric methods in nonlinear analysis, Grundlehren Math. Wissen., 263, Springer-Verlag, Berlin, 1984

[27] Krstić, M.; Kanellakopoulos, I.; Kokotović, P. Nonlinear and adaptive control design, Wiley, New York, 1995

[28] Kurzweil, Jaroslav On the inversion of Lyapunov’s second theorem on stability of motion, Czechoslovak Mathematical Journal, Volume 06 (1956) no. 2, pp. 217-259 http://eudml.org/doc/11835 Amer. Math. Soc. Transl. series, vol. 24 (1956), p. 19-77 | DOI

[29] Lions, J.-L. Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., Volume 30 (1988) no. 1, pp. 1-68 | DOI | MR | Zbl

[30] Martin, Ph.; Rouchon, Pierre Systèmes plats : planification et suivi de trajectoires, Aspects de la théorie du contrôle (Journées X-UPS), Les Éditions de l’École Polytechnique, Palaiseau, 1999 (ce volume) | DOI

[31] Morin, P.; Samson, C. Time-varying exponential stabilization of a rigid spacecraft with two control torques, IEEE Trans. Automat. Control, Volume 42 (1997) no. 4, pp. 528-534 | DOI | MR | Zbl

[32] Morin, P.; Samson, C.; Pomet, J.-B.; Jiang, Z.-P. Time-varying feedback stabilization of the attitude of a rigid spacecraft with two controls, Systems Control Lett., Volume 25 (1995) no. 5, pp. 375-385 | DOI | MR | Zbl

[33] Nagano, Tadashi Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan, Volume 18 (1966), pp. 398-404 | DOI | MR | Zbl

[34] Nijmeijer, Henk; van der Schaft, Arjan Nonlinear dynamical control systems, Springer-Verlag, New York, 1990 | DOI

[35] Puel, J.-P. Contrôle et équations aux dérivées partielles, Aspects de la théorie du contrôle (Journées X-UPS), Les Éditions de l’École Polytechnique, Palaiseau, 1999 (ce volume) | DOI

[36] Rashevski, P. K. About connecting two points of complete nonholonomic space by admissible curve, Uch Zapiski ped. inst. Libknexta, Volume 2 (1938), pp. 83-94

[37] Samson, Claude Velocity and torque feedback control of a nonholonomic cart, Advanced robot control. Proc. of the intl. workshop on nonlinear and adaptive control : issues in robotics (Grenoble, Nov. 21-23, 1990), Springer-Verlag, Berlin, 1991, pp. 125-151 | MR | Zbl

[38] Sepulchre, R.; Janković, M.; Kokotović, P. V. Constructive nonlinear control, Commun. and Control Engineering Series, Springer-Verlag, Berlin, 1997 | DOI

[39] Sontag, Eduardo; Sussmann, Hector Remarks on continuous feedback, 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes (1980), pp. 916-921 | DOI

[40] Sussmann, H. J. A general theorem on local controllability, SIAM J. Control Optim., Volume 25 (1987) no. 1, pp. 158-194 | DOI | MR | Zbl

[41] Teel, Andrew; Praly, Laurent Global stabilizability and observability imply semi-global stabilizability by output feedback, Systems Control Lett., Volume 22 (1994) no. 5, pp. 313-325 | DOI | MR | Zbl