Nearly time optimal stabilizing patchy feedbacks
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 2, pp. 279-310.
@article{AIHPC_2007__24_2_279_0,
     author = {Ancona, Fabio and Bressan, Alberto},
     title = {Nearly time optimal stabilizing patchy feedbacks},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {279--310},
     publisher = {Elsevier},
     volume = {24},
     number = {2},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.03.010},
     mrnumber = {2310696},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.010/}
}
TY  - JOUR
AU  - Ancona, Fabio
AU  - Bressan, Alberto
TI  - Nearly time optimal stabilizing patchy feedbacks
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 279
EP  - 310
VL  - 24
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.010/
DO  - 10.1016/j.anihpc.2006.03.010
LA  - en
ID  - AIHPC_2007__24_2_279_0
ER  - 
%0 Journal Article
%A Ancona, Fabio
%A Bressan, Alberto
%T Nearly time optimal stabilizing patchy feedbacks
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 279-310
%V 24
%N 2
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.010/
%R 10.1016/j.anihpc.2006.03.010
%G en
%F AIHPC_2007__24_2_279_0
Ancona, Fabio; Bressan, Alberto. Nearly time optimal stabilizing patchy feedbacks. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 2, pp. 279-310. doi : 10.1016/j.anihpc.2006.03.010. http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.010/

[1] Ancona F., Bressan A., Patchy vector fields and asymptotic stabilization, ESAIM Control Optim. Calc. Var. 4 (1999) 445-471. | Numdam | MR | Zbl

[2] Ancona F., Bressan A., Flow stability of patchy vector fields and robust feedback stabilization, SIAM J. Control Optim. 41 (5) (2003) 1455-1476. | MR | Zbl

[3] Ancona F., Bressan A., Stability rates for patchy vector fields, ESAIM Control Optim. Calc. Var. 10 (2) (2004) 168-200. | Numdam | MR | Zbl

[4] Ancona F., Bressan A., Stabilization by patchy feedbacks and robustness properties, in: De Queiroz M.S., Malisoff M.A., Wolenski P.R. (Eds.), Optimal Control, Stabilization and Nonsmooth Analysis, Proceedings of “Louisiana Conference in Mathematical Control Theory (MCT'03)”, Lectures Notes in Control and Inform. Sci., vol. 301, Springer-Verlag, Heidelberg, 2004, pp. 185-200.

[5] Bardi M., Capuzzo Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser Boston, Boston, MA, 1997. | Zbl

[6] Berkovitz L.D., Optimal Control Theory, Applied Mathematical Sciences, vol. 12, Springer-Verlag, New York, 1974. | MR | Zbl

[7] Berkovitz L.D., Optimal feedback controls, SIAM J. Control Optim. 27 (5) (1989) 991-1006. | MR | Zbl

[8] Boltyanskii V.G., Optimal feedback controls, SIAM J. Control 4 (1966) 326-361.

[9] Boscain U., Piccoli B., Optimal Syntheses for Control Systems on 2-D Manifolds, Mathematiques & Applications, vol. 43, Springer-Verlag, Berlin, 2004. | MR

[10] Bressan A., Singularities of stabilizing feedbacks, Control Theory and its Applications (Grado, 1998). Rend. Sem. Mat. Univ. Politec. Torino 56 (4) (1998) 87-104. | MR | Zbl

[11] Bressan A., Piccoli B., A generic classification of time-optimal planar stabilizing feedbacks, SIAM J. Control Optim. 36 (1) (1998) 12-32. | MR | Zbl

[12] Brunovský P., Existence of regular synthesis for general control problems, J. Differential Equations 38 (3) (1980) 317-343. | MR | Zbl

[13] Cannarsa P., Frankowska H., Some characterization of optimal trajectories on control theory, SIAM J. Control Optim. 29 (6) (1991) 1322-1347. | MR | Zbl

[14] 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. | Zbl

[15] Clarke F.H., Ledyaev Yu.S., Rifford L., Stern R.J., Feedback stabilization and Lyapunov functions, SIAM J. Control Optim. 39 (1) (2000) 25-48. | MR | Zbl

[16] Clarke F.H., Ledyaev Yu.S., Sontag E.D., Subbotin A.I., Asymptotic controllability implies feedback stabilization, IEEE Trans. Autom. Control 42 (1997) 1394-1407. | MR | Zbl

[17] Clarke F.H., Rifford L., Stern R.J., Feedback in state constrained optimal control, ESAIM Control Optim. Calc. Var. 7 (2002) 97-134. | Numdam | MR | Zbl

[18] Clarke F.H., Ledyaev Yu.S., Stern R.J., Wolenski P.R., Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, vol. 178, Springer-Verlag, New York, 1998. | MR | Zbl

[19] Ishii H., Koike S., On ϵ-optimal controls for state constraints problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (4) (2000) 473-502. | Numdam | Zbl

[20] Krasovskii N.N., Differential games. Approximate and formal models, Mat. Sb. 6 (4) (1978) 541-571, English translation:, Math. USSR-Sb. 35 (6) (1979) 795-822. | MR | Zbl

[21] Krasovskii N.N., Extremal aiming and extremal displacement in a game-theoretical control, Problems Control Inform. Theory 13 (5) (1984) 287-302. | MR | Zbl

[22] Krasovskii N.N., Subbotin A.I., Positional Differential Games, Nauka, Moscow, 1974, (in Russian). | MR | Zbl

[23] Launay G., Pelletier L., The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two, J. Dynam. Control Systems 3 (2) (1997) 165-203. | MR | Zbl

[24] Marchal C., Chattering arcs and chattering controls, J. Optim. Theory Appl. 11 (1973) 441-468. | MR | Zbl

[25] Marigo A., Piccoli B., Regular syntheses and solutions to discontinuous ODEs, ESAIM Control Optim. Calc. Var. 7 (2002) 291-307. | Numdam | MR | Zbl

[26] Nobakhtian S., Stern R.J., Universal near-optimal feedbacks, J. Optim. Theory Appl. 107 (1) (2000) 89-122. | MR | Zbl

[27] Piccoli B., Regular time-optimal syntheses for smooth planar systems, Rend. Sem. Mat. Univ. Padova 95 (1996) 59-79. | Numdam | MR | Zbl

[28] Piccoli B., Classification of generic singularities for the planar time-optimal synthesis, SIAM J. Control Optim. 34 (6) (1996) 1914-1946. | MR | Zbl

[29] Piccoli B., Sussmann H., Regular synthesis and sufficiency conditions for optimality, SIAM J. Control Optim. 39 (2) (2000) 359-410. | MR | Zbl

[30] Rifford L., Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim. 41 (3) (2000) 659-681. | MR | Zbl

[31] Rowland J.D., Vinter R.B., Construction of optimal feedback controls, Systems Control Lett. 16 (5) (1991) 357-367. | MR | Zbl

[32] Sontag E.D., Mathematical Control Theory. Deterministic Finite Dimensional Systems, Texts in Applied Mathematics, vol. 6, second ed., Springer-Verlag, New York, 1998. | MR | Zbl

[33] Sontag E.D., Stability and stabilization: discontinuities and the effect of disturbances, in: Clarke F.H., Stern R.J. (Eds.), Nonlinear Analysis, Differential Equations, and Control, Proc. NATO Advanced Study Institute, Montreal, Jul/Aug 1998, Kluwer, 1999, pp. 551-598. | MR | Zbl

[34] Sussmann H.J., Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets, in: Sussmann H.J. (Ed.), Nonlinear Controllability and Optimal Control, Dekker, New York, 1990, pp. 1-19. | MR | Zbl

[35] Zelikin M.I., Borisov V.F., Theory of Chattering Control. With Applications to Astronautics, Robotics, Economics, and Engineering, Systems & Control: Foundations & Applications, vol. 43, Birkhäuser Boston, Boston, MA, 1994. | MR | Zbl

Cité par Sources :