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State constrained patchy feedback stabilization
1. | Istituto per le Applicazioni del Calcolo “M. Picone", Consiglio Nazionale delle Ricerche, Via dei Taurini 19, I-00185 Roma, Italy |
References:
[1] |
F. Ancona and A. Bressan, Patchy vector fields and asymptotic stabilization, ESAIM Control Optim. Calc. Var., 4 (1999), 445-471.
doi: 10.1051/cocv:1999117. |
[2] |
F. Ancona and A. Bressan, Flow stability of patchy vector fields and robust feedback stabilization, SIAM J. Control Optim., 41 (2002), 1455-1476.
doi: 10.1137/S0363012901391676. |
[3] |
F. Ancona and A. Bressan, Nearly time optimal stabilizing patchy feedbacks, Ann. Inst. Henri Poincaré, Analyse Non Linéaire, 24 (2007), 279-310.
doi: 10.1016/j.anihpc.2006.03.010. |
[4] |
F. Ancona and A. Bressan, Patchy feedbacks for stabilization and optimal control: General theory and robustness properties, in Geometric Control and Nonsmooth Analysis, Ser. Adv. Math. Appl. Sci., 76, World Sci. Publ., Hackensack, NJ, 2008, 28-64.
doi: 10.1142/9789812776075_0002. |
[5] |
A. M. Bloch and S. Drakunov, Stabilization and tracking in the nonholonomic integrator via sliding modes, Systems Control Lett., 29 (1996), 91-99.
doi: 10.1016/S0167-6911(96)00049-7. |
[6] |
A. Bressan, Singularities of stabilizing feedbacks, Rend. Sem. Mat. Univ. Politec. Torino, 56 (1998), 87-104. |
[7] |
A. Bressan and B. Piccoli, Introduction to the Mathematical Theory of Control, AIMS Series on Applied Mathematics, 2, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2007. |
[8] |
A. Bressan and F. S. Priuli, Nearly optimal patchy feedbacks, Discr. Cont. Dyn. Systems Series A, 21 (2008), 687-701.
doi: 10.3934/dcds.2008.21.687. |
[9] |
R. W. Brockett, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory (eds. R. W. Brockett, R. S. Millman and H. J. Sussmann), Progr. Math., 27, Birkhaüser, Boston, MA, 1983, 181-191. |
[10] |
F. H. Clarke, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, 178, Springer-Verlag, New York, 1998. |
[11] |
F. H. Clarke, L. Rifford and R. J. Stern, Feedback in state constrained optimal control, ESAIM Control Optim. Calc. Var., 7 (2002), 97-133.
doi: 10.1051/cocv:2002005. |
[12] |
F. H. Clarke and R. J. Stern, State constrained feedback stabilization, SIAM J. Control Optim., 42 (2003), 422-441.
doi: 10.1137/S036301290240453X. |
[13] |
F. H. Clarke and R. J. Stern, Lyapunov feedback characterizations state constrained controllability stabilization, Systems and Control Letters, 54 (2005), 747-752.
doi: 10.1016/j.sysconle.2004.11.013. |
[14] |
J.-M. Coron, Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, 5 (1992), 295-312.
doi: 10.1007/BF01211563. |
[15] |
J.-M. Coron, On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback law, SIAM J. Control Optim., 33 (1995), 804-833.
doi: 10.1137/S0363012992240497. |
[16] |
S. Drakunov and V. I. Utkin, Sliding-mode observers: Tutorial, in Proceedings of the 34th IEEE Conference of Decision and Control, IEEE Publications, 4, Piscataway, NJ, 1995, 3376-3378.
doi: 10.1109/CDC.1995.479009. |
[17] |
R. Goebel, C. Prieur and A. R. Teel, Hybrid feedback control and robust stabilization of nonlinear systems, IEEE Trans. Autom. Control, 52 (2007), 2103-2117.
doi: 10.1109/TAC.2007.908320. |
[18] |
R. Goebel and A. R. Teel, Direct design of robustly asymptotically stabilizing hybrid feedback, ESAIM Control Optim. Calc. Var., 15 (2009), 205-213.
doi: 10.1051/cocv:2008023. |
[19] |
R. T. Rockafellar, Clarke's tangent cones and the boundaries of closed sets in $\mathbbR^n$, Nonlinear Anal., 3 (1979), 145-154.
doi: 10.1016/0362-546X(79)90044-0. |
[20] |
E. D. Sontag, Stability and stabilization: Discontinuities and the effect of disturbances, in Nonlinear Analysis, Differential Equations, and Control (eds. F. H. Clarke and R. J. Stern), NATO Sci. Ser. C Math. Phys. Sci., 528, Kluwer Academic, Dordrecht, 1999, 551-598. |
[21] |
E. D. Sontag and H. J. Sussmann, Remarks on continuous feedback, in Proceedings of the 19th IEEE Conference on Decision and Control, IEEE Publications, Piscataway, NJ, 1980, 916-921.
doi: 10.1109/CDC.1980.271934. |
[22] |
H. J. Sussmann, Subanalytic sets and feedback control, J. Differential Equations, 31 (1979), 31-52.
doi: 10.1016/0022-0396(79)90151-7. |
show all references
References:
[1] |
F. Ancona and A. Bressan, Patchy vector fields and asymptotic stabilization, ESAIM Control Optim. Calc. Var., 4 (1999), 445-471.
doi: 10.1051/cocv:1999117. |
[2] |
F. Ancona and A. Bressan, Flow stability of patchy vector fields and robust feedback stabilization, SIAM J. Control Optim., 41 (2002), 1455-1476.
doi: 10.1137/S0363012901391676. |
[3] |
F. Ancona and A. Bressan, Nearly time optimal stabilizing patchy feedbacks, Ann. Inst. Henri Poincaré, Analyse Non Linéaire, 24 (2007), 279-310.
doi: 10.1016/j.anihpc.2006.03.010. |
[4] |
F. Ancona and A. Bressan, Patchy feedbacks for stabilization and optimal control: General theory and robustness properties, in Geometric Control and Nonsmooth Analysis, Ser. Adv. Math. Appl. Sci., 76, World Sci. Publ., Hackensack, NJ, 2008, 28-64.
doi: 10.1142/9789812776075_0002. |
[5] |
A. M. Bloch and S. Drakunov, Stabilization and tracking in the nonholonomic integrator via sliding modes, Systems Control Lett., 29 (1996), 91-99.
doi: 10.1016/S0167-6911(96)00049-7. |
[6] |
A. Bressan, Singularities of stabilizing feedbacks, Rend. Sem. Mat. Univ. Politec. Torino, 56 (1998), 87-104. |
[7] |
A. Bressan and B. Piccoli, Introduction to the Mathematical Theory of Control, AIMS Series on Applied Mathematics, 2, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2007. |
[8] |
A. Bressan and F. S. Priuli, Nearly optimal patchy feedbacks, Discr. Cont. Dyn. Systems Series A, 21 (2008), 687-701.
doi: 10.3934/dcds.2008.21.687. |
[9] |
R. W. Brockett, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory (eds. R. W. Brockett, R. S. Millman and H. J. Sussmann), Progr. Math., 27, Birkhaüser, Boston, MA, 1983, 181-191. |
[10] |
F. H. Clarke, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, 178, Springer-Verlag, New York, 1998. |
[11] |
F. H. Clarke, L. Rifford and R. J. Stern, Feedback in state constrained optimal control, ESAIM Control Optim. Calc. Var., 7 (2002), 97-133.
doi: 10.1051/cocv:2002005. |
[12] |
F. H. Clarke and R. J. Stern, State constrained feedback stabilization, SIAM J. Control Optim., 42 (2003), 422-441.
doi: 10.1137/S036301290240453X. |
[13] |
F. H. Clarke and R. J. Stern, Lyapunov feedback characterizations state constrained controllability stabilization, Systems and Control Letters, 54 (2005), 747-752.
doi: 10.1016/j.sysconle.2004.11.013. |
[14] |
J.-M. Coron, Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, 5 (1992), 295-312.
doi: 10.1007/BF01211563. |
[15] |
J.-M. Coron, On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback law, SIAM J. Control Optim., 33 (1995), 804-833.
doi: 10.1137/S0363012992240497. |
[16] |
S. Drakunov and V. I. Utkin, Sliding-mode observers: Tutorial, in Proceedings of the 34th IEEE Conference of Decision and Control, IEEE Publications, 4, Piscataway, NJ, 1995, 3376-3378.
doi: 10.1109/CDC.1995.479009. |
[17] |
R. Goebel, C. Prieur and A. R. Teel, Hybrid feedback control and robust stabilization of nonlinear systems, IEEE Trans. Autom. Control, 52 (2007), 2103-2117.
doi: 10.1109/TAC.2007.908320. |
[18] |
R. Goebel and A. R. Teel, Direct design of robustly asymptotically stabilizing hybrid feedback, ESAIM Control Optim. Calc. Var., 15 (2009), 205-213.
doi: 10.1051/cocv:2008023. |
[19] |
R. T. Rockafellar, Clarke's tangent cones and the boundaries of closed sets in $\mathbbR^n$, Nonlinear Anal., 3 (1979), 145-154.
doi: 10.1016/0362-546X(79)90044-0. |
[20] |
E. D. Sontag, Stability and stabilization: Discontinuities and the effect of disturbances, in Nonlinear Analysis, Differential Equations, and Control (eds. F. H. Clarke and R. J. Stern), NATO Sci. Ser. C Math. Phys. Sci., 528, Kluwer Academic, Dordrecht, 1999, 551-598. |
[21] |
E. D. Sontag and H. J. Sussmann, Remarks on continuous feedback, in Proceedings of the 19th IEEE Conference on Decision and Control, IEEE Publications, Piscataway, NJ, 1980, 916-921.
doi: 10.1109/CDC.1980.271934. |
[22] |
H. J. Sussmann, Subanalytic sets and feedback control, J. Differential Equations, 31 (1979), 31-52.
doi: 10.1016/0022-0396(79)90151-7. |
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