Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 1-35.
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     author = {Morin, Pascal and Samson, Claude},
     title = {Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1--35},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     mrnumber = {1680693},
     zbl = {0919.93059},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1999__4__1_0/}
}
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Morin, Pascal; Samson, Claude. Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 1-35. http://www.numdam.org/item/COCV_1999__4__1_0/

[1] M.K. Bennani and P. Rouchon, Robust stabilization of flat and chained systems, in European Control Conference (ECC) ( 1995) 2642-2646.

[2] R.W. Brockett, Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, R.S. Millman R.W. Brockett and H.H. Sussmann Eds., Birkauser ( 1983). | MR | Zbl

[3] C. Canudas De Wit and O. J. Sørdalen, Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Trans. Automat. Control 37 ( 1992) 1791-1797. | MR | Zbl

[4] M. Fliess, J. Lévine, P. Martin and P. Rouchon, Flatness and defect of non-linear systems: introductory theory and examples. Internat. J. Control 61 ( 1995) 1327-1361. | MR | Zbl

[5] H. Hermes, Nilpotent and high-order approximations of vector field systems. SIAM Rev. 33 ( 1991) 238-264. | MR | Zbl

[6] A. Isidori, Nonlinear control systems. Springer Verlag, third edition ( 1995). | MR | Zbl

[7] M. Kawski, Geometric homogeneity and stabilization, in IFAC Nonlinear Control Systems Design Symp. (NOLCOS) ( 1995) 164-169.

[8] I. Kolmanovsky and N.H. Mcclamroch, Developments in nonholonomic control problems. IEEE Control Systems ( 1995) 20-36.

[9] J. Kurzweil and J. Jarnik, Iterated lie brackets in limit processes in ordinary differential equations. Results in Mathematics 14 ( 1988) 125-137. | MR | Zbl

[10] Z. Li and J.F. Canny, Nonholonomic motion planning. Kluwer Academic Press ( 1993). | Zbl

[11] W. Liu, An approximation algorithm for nonholonomic systems. SIAM J. Contr. Opt. 35 ( 19971328-1365. | MR | Zbl

[12] D.A. Lizárraga, P. Morin and C. Samson, Non-robustness of continuous homogeneous stabilizers for affine systems. Technical Report 3508, INRIA ( 1998) Available at http://www.inria.fr/RRRT/RR-3508.html

[13] R.T. M'Closkey and R.M. Murray, Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Trans. Automat. Contr. 42 ( 1997) 614-628. | MR | Zbl

[14] S. Monaco and D. Normand-Cyrot, An introduction to motion planning using multirate digital control, in IEEE Conf. on Decision and Control (CDC) ( 1991) 1780-1785.

[15] P. Morin, J.-B. Pomet and C. Samson, Design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of lie brackets in closed-loop. SIAM J. Contr. Opt. (to appear). | MR | Zbl

[16] P. Morin, J.-B. Pomet and C. Samson, Developments in time-varying feedback stabilization of nonlinear systems, in IFAC Nonlinear Control Systems Design Symp. (NOLCOS) ( 1998) 587-594.

[17] P. Morin and C. Samson, Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics. Technical Report 3477, INRIA ( 1998).

[18] R.M. Murray and S.S. Sastry, Nonholonomic motion planning: Steering using sinusoids. EEE Trans. Automat. Contr. 38 ( 1993) 700-716. | MR | Zbl

[19] L. Rosier, Étude de quelques problèmes de stabilisation. PhD thesis, École Normale de Cachan ( 1993).

[20] C. Samson, Velocity and torque feedback control of a nonholonomic cart, in Int. Workshop in Adaptative and Nonlinear Control: Issues in Robotics. LNCIS, Vol. 162, Springer Verlag, 1991 ( 1990). | MR | Zbl

[21] O.J. Sørdalen and O. Egeland, Exponential stabilization of nonholonomic chained systems. IEEE Trans. Automat. Contr. 40 ( 1995) 35-49. | MR | Zbl

[22] G. Stefani, Polynomial approximations to control systems and local controllability, in IEEE Conf. on Decision and Control (CDC) ( 1985) 33-38.

[23] G. Stefani, On the local controllability of scalar-input control systems, in Theory and Applications of Nonlinear Control Systems, Proc. of MTNS'84, C.I. Byrnes and A. Linsquist Eds., North-Holland ( 1986) 167-179. | MR | Zbl

[24] H.J. Sussmann and W. Liu, Limits of highly oscillatory controls ans approximation of general paths by admissible trajectories, in IEEE Conf. on Decision and Control (CDC) ( 1991) 437-442.

[25] H.J. Sussmann, Lie brackets and local controllability: a sufficient condition for scalar-input systems, SIAM J. Contr. Opt. 21 ( 1983) 686-713. | MR | Zbl

[26] H.J. Sussmann, A general theorem on local controllability. SIAM J. Contr. Opt. 25 ( 1987) 158-194. | MR | Zbl