@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://www.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://www.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://www.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://www.numdam.org/articles/10.1016/j.anihpc.2006.03.010/
[1] Patchy vector fields and asymptotic stabilization, ESAIM Control Optim. Calc. Var. 4 (1999) 445-471. | Numdam | MR | Zbl
, ,[2] Flow stability of patchy vector fields and robust feedback stabilization, SIAM J. Control Optim. 41 (5) (2003) 1455-1476. | MR | Zbl
, ,[3] Stability rates for patchy vector fields, ESAIM Control Optim. Calc. Var. 10 (2) (2004) 168-200. | Numdam | MR | Zbl
, ,[4] Stabilization by patchy feedbacks and robustness properties, in: , , (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] Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser Boston, Boston, MA, 1997. | Zbl
, ,[6] Optimal Control Theory, Applied Mathematical Sciences, vol. 12, Springer-Verlag, New York, 1974. | MR | Zbl
,[7] Optimal feedback controls, SIAM J. Control Optim. 27 (5) (1989) 991-1006. | MR | Zbl
,[8] Optimal feedback controls, SIAM J. Control 4 (1966) 326-361.
,[9] Optimal Syntheses for Control Systems on 2-D Manifolds, Mathematiques & Applications, vol. 43, Springer-Verlag, Berlin, 2004. | MR
, ,[10] 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] A generic classification of time-optimal planar stabilizing feedbacks, SIAM J. Control Optim. 36 (1) (1998) 12-32. | MR | Zbl
, ,[12] Existence of regular synthesis for general control problems, J. Differential Equations 38 (3) (1980) 317-343. | MR | Zbl
,[13] Some characterization of optimal trajectories on control theory, SIAM J. Control Optim. 29 (6) (1991) 1322-1347. | MR | Zbl
, ,[14] 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] Feedback stabilization and Lyapunov functions, SIAM J. Control Optim. 39 (1) (2000) 25-48. | MR | Zbl
, , , ,[16] Asymptotic controllability implies feedback stabilization, IEEE Trans. Autom. Control 42 (1997) 1394-1407. | MR | Zbl
, , , ,[17] Feedback in state constrained optimal control, ESAIM Control Optim. Calc. Var. 7 (2002) 97-134. | Numdam | MR | Zbl
, , ,[18] Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, vol. 178, Springer-Verlag, New York, 1998. | MR | Zbl
, , , ,[19] On ϵ-optimal controls for state constraints problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (4) (2000) 473-502. | Numdam | Zbl
, ,[20] 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] Extremal aiming and extremal displacement in a game-theoretical control, Problems Control Inform. Theory 13 (5) (1984) 287-302. | MR | Zbl
,[22] Positional Differential Games, Nauka, Moscow, 1974, (in Russian). | MR | Zbl
, ,[23] 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] Chattering arcs and chattering controls, J. Optim. Theory Appl. 11 (1973) 441-468. | MR | Zbl
,[25] Regular syntheses and solutions to discontinuous ODEs, ESAIM Control Optim. Calc. Var. 7 (2002) 291-307. | Numdam | MR | Zbl
, ,[26] Universal near-optimal feedbacks, J. Optim. Theory Appl. 107 (1) (2000) 89-122. | MR | Zbl
, ,[27] Regular time-optimal syntheses for smooth planar systems, Rend. Sem. Mat. Univ. Padova 95 (1996) 59-79. | Numdam | MR | Zbl
,[28] Classification of generic singularities for the planar time-optimal synthesis, SIAM J. Control Optim. 34 (6) (1996) 1914-1946. | MR | Zbl
,[29] Regular synthesis and sufficiency conditions for optimality, SIAM J. Control Optim. 39 (2) (2000) 359-410. | MR | Zbl
, ,[30] Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim. 41 (3) (2000) 659-681. | MR | Zbl
,[31] Construction of optimal feedback controls, Systems Control Lett. 16 (5) (1991) 357-367. | MR | Zbl
, ,[32] Mathematical Control Theory. Deterministic Finite Dimensional Systems, Texts in Applied Mathematics, vol. 6, second ed., Springer-Verlag, New York, 1998. | MR | Zbl
,[33] Stability and stabilization: discontinuities and the effect of disturbances, in: , (Eds.), Nonlinear Analysis, Differential Equations, and Control, Proc. NATO Advanced Study Institute, Montreal, Jul/Aug 1998, Kluwer, 1999, pp. 551-598. | MR | Zbl
,[34] Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets, in: (Ed.), Nonlinear Controllability and Optimal Control, Dekker, New York, 1990, pp. 1-19. | MR | Zbl
,[35] 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
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