Stratified semiconcave control-Lyapunov functions and the stabilization problem

Ludovic Rifford

Annales de l'I.H.P. Analyse non linéaire (2005)

  • Volume: 22, Issue: 3, page 343-384
  • ISSN: 0294-1449

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Rifford, Ludovic. "Stratified semiconcave control-Lyapunov functions and the stabilization problem." Annales de l'I.H.P. Analyse non linéaire 22.3 (2005): 343-384. <http://eudml.org/doc/78660>.

@article{Rifford2005,
author = {Rifford, Ludovic},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Control-Lyapunov function; Semiconcave function; Feedback stabilization},
language = {eng},
number = {3},
pages = {343-384},
publisher = {Elsevier},
title = {Stratified semiconcave control-Lyapunov functions and the stabilization problem},
url = {http://eudml.org/doc/78660},
volume = {22},
year = {2005},
}

TY - JOUR
AU - Rifford, Ludovic
TI - Stratified semiconcave control-Lyapunov functions and the stabilization problem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2005
PB - Elsevier
VL - 22
IS - 3
SP - 343
EP - 384
LA - eng
KW - Control-Lyapunov function; Semiconcave function; Feedback stabilization
UR - http://eudml.org/doc/78660
ER -

References

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  1. [1] Albano P., Cannarsa P., Structural properties of singularities of semiconcave functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)28 (4) (1999) 719-740. Zbl0957.26002MR1760538
  2. [2] Alberti G., Ambrosio L., Cannarsa P., On the singularities of convex functions, Manuscripta Math.76 (3–4) (1992) 421-435. Zbl0784.49011MR1185029
  3. [3] Ancona F., Bressan A., Patchy vector fields and asymptotic stabilization, ESAIM Control Optim. Calc. Var.4 (1999) 445-471. Zbl0924.34058MR1693900
  4. [4] Astolfi A., Discontinuous control of nonholonomic systems, Systems Control Lett.27 (1) (1996) 37-45. Zbl0877.93107MR1375910
  5. [5] Aubin J.-P., Viability Theory, Birkhäuser Boston, Boston MA, 1991. Zbl0755.93003MR1134779
  6. [6] Bardi M., Capuzzo-Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations, Birkhäuser Boston, Boston, MA, 1997. Zbl0890.49011MR1484411
  7. [7] Brockett R.W., Asymptotic stability and feedback stabilization, in: Brockett R.W., Millman R.S., Sussmann H.J. (Eds.), Differential Geometric Control Theory, Birkhäuser, Boston, 1983, pp. 181-191. Zbl0528.93051MR708502
  8. [8] Cannarsa P., Sinestrari C., Semiconcave Functions, Hamilton–Jacobi Equations, and Optimal Control, Progress in Nonlinear Differential Equations and Their Applications, vol. 58, Birkhäuser Boston, Boston, MA, 2004. Zbl1095.49003MR2041617
  9. [9] Clarke F.H., Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983. Zbl0582.49001MR709590
  10. [10] Clarke F.H., Ledyaev Yu.S., Sontag E.D., Subbotin A.I., Asymptotic controllability implies feedback stabilization, IEEE Trans. Automat. Control42 (1997) 1394-1407. Zbl0892.93053MR1472857
  11. [11] Clarke F.H., Ledyaev Yu.S., Stern R.J., Wolenski P.R., Nonsmooth Analysis and Control Theory, Graduate Texts in Math., vol. 178, Springer-Verlag, New York, 1998. Zbl1047.49500MR1488695
  12. [12] Clarke F.H., Stern R.J., Wolenski P.R., Proximal smoothness and the lower- C 2 property, J. Convex Anal.2 (1995) 117-145. Zbl0881.49008MR1363364
  13. [13] Coron J.-M., On the stabilization of some nonlinear control systems: results, tools, and applications, in: Nonlinear Analysis, Differential Equations and Control (Montreal, QC, 1998), Kluwer Academic, Dordrecht, 1999, pp. 307-367. Zbl0984.93067MR1695009
  14. [14] Crandall M.G., Lions P.-L., Viscosity solutions of Hamilton–Jacobi equations, Trans. Amer. Math. Soc.277 (1) (1983) 1-42. Zbl0599.35024MR690039
  15. [15] Gantmacher F.R., The Theory of Matrices. Vol. 1, AMS Chelsea Publishing, Providence, RI, 1998. Zbl0927.15001MR1657129
  16. [16] Goresky M., MacPherson R., Stratified Morse Theory, Springer-Verlag, Berlin, 1988. Zbl0639.14012MR932724
  17. [17] Lions P.-L., Generalized Solutions of Hamilton–Jacobi Equations, Pitman, Boston, MA, 1982, (Advanced Publishing Program). Zbl0497.35001MR667669
  18. [18] Michael E., Continuous selections. I, Ann. of Math. (2)63 (1956) 361-382. Zbl0071.15902MR77107
  19. [19] Rantzer A., A dual to Lyapunov stability theorem, Systems Control Lett.42 (3) (2000) 161-168. Zbl0974.93058MR2007046
  20. [20] A. Rantzer, A converse Lyapunov stability theorem, Personnal communication. 
  21. [21] L. Rifford, Problèmes de stabilisation en théorie du controle, PhD thesis, Université Claude Bernard Lyon I, 2000. 
  22. [22] Rifford L., Stabilisation des systèmes globalement asymptotiquement commandables, C. R. Acad. Sci. Paris Sér. I Math.330 (3) (2000) 211-216. Zbl0952.93113MR1748310
  23. [23] Rifford L., Existence of Lipschitz and semiconcave control-Lyapunov functions, SIAM J. Control Optim.39 (4) (2000) 1043-1064. Zbl0982.93068MR1814266
  24. [24] Rifford L., Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim.41 (3) (2002) 659-681. Zbl1034.93053MR1939865
  25. [25] Rifford L., Singularities of viscosity solutions and the stabilization problem in the plane, Indiana Univ. Math. J.52 (5) (2003) 1373-1396. Zbl1119.93058MR2010731
  26. [26] Rifford L., A Morse–Sard theorem for the distance function on Riemannian manifolds, Manuscripta Math.113 (2004) 251-265. Zbl1051.53050MR2128549
  27. [27] L. Rifford, On the existence of local smooth repulsive stabilizing feedbacks in dimension three, in preparation. Zbl1134.93401
  28. [28] L. Rifford, The stabilization problem on surfaces, Rend. Semin. Mat. Torino, submitted for publication. Zbl1170.93367
  29. [29] Rockafellar R.T., Convex Analysis, Princeton University Press, Princeton, NJ, 1997, Reprint of the 1970 original, Princeton Paperbacks. Zbl0193.18401MR1451876
  30. [30] Sontag E.D., A Lyapunov-like characterization of asymptotic controllability, SIAM J. Control Optim.21 (1983) 462-471. Zbl0513.93047MR696908
  31. [31] Sontag E.D., Stability and stabilization: discontinuities and the effect of disturbances, in: Nonlinear Analysis, Differential Equations and Control (Montreal, QC, 1998), Kluwer Academic, Dordrecht, 1999, pp. 307-367. Zbl0937.93034MR1695014
  32. [32] Sontag E.D., Clocks and insensitivity to small measurement errors, ESAIM Control Optim. Calc. Var.4 (1999) 537-557. Zbl0984.93068MR1746166
  33. [33] Sussmann H.J., Subanalytic sets and feedback control, J. Differential Equations31 (1) (1979) 31-52. Zbl0407.93010MR524816

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