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La régularité lipshtzienne des courbes minimisantes pour un problème de contrôle optimale géométrique

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par Nedjoua Driai
Université de Sétif - Algerie - magister 2005
  

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Bibliographie

[1] Riccardo ADAMi et Ugo BoSCAiN : Controllability of the Schrödinger equation via intersection of eigenvalues. In Proceedings of the 44th IEEE Conference on Decision and Control, pages 1080-1085, 2005.

[2] Shmuel AGMoN : Bounds on exponential decay of eigenfunctions of Schrödinger operators. In Schrödinger operators (Como, 1984), volume 1159 de Lecture Notes in Math., pages 1- 38. Springer, Berlin, 1985.

[3] Andrei AGRACHEv et Thomas CHAMBRioN : An estimation of the controllability time for single-input systems on compact Lie groups. ESAIM Control Optim. Calc. Var., 12(3):409- 441, 2006.

[4] Andrei A. AGRACHEv : A «Gauss-Bonnet formula» for contact sub-Riemannian manifolds. Dokl. Akad. Nauk, 381(5):583-585, 2001.

[5] Andrei A. AGRACHEv et Daniel LiBERzoN : Lie-algebraic stability criteria for switched systems. SIAM J. Control Optim., 40(1):253-269, 2001.

[6] Andrei A. AGRACHEv et Yuri L. SACHKov : Control theory from the geometric viewpoint, volume 87 de Encyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin, 2004. Control Theory and Optimization, II.

[7] Andrey A. AGRACHEv et Andrey V. SARyCHEv : Controllability of 2D Euler and NavierStokes equations by degenerate forcing. Comm. Math. Phys., 265(3):673-697, 2006.

[8] Jeffrey H. ALBERT : Genericity of simple eigenvalues for elliptic PDE's. Proc. Amer. Math. Soc., 48:413-418, 1975.

[9] Francesca ALBERTiNi et Domenico D'ALESSANDRo : Notions of controllability for bilinear multilevel quantum systems. IEEE Trans. Automat. Control, 48(8):1399-1403, 2003.

[10] François ALouGES, Antonio DESiMoNE et Aline LEFEBvRE : Optimal strokes for low Reynolds number swimmers : an example. J. Nonlinear Sci., 18(3):277-302, 2008.

[11] Claudio ALTAFiNi : Controllability properties for finite dimensional quantum Markovian master equations. J. Math. Phys., 44(6):23572372, 2003.

[12] B. D. O. ANDERSoN, R. R. BiTMEAD, C. R. JoHNSoN, P. V. KoKoToviC, R. L. KoSuT, I. M. Y. MAREELS, L. PRALy et B. D. RiEDLE : Stability of adaptive systems : Passivity and averaging analysis. MIT Press, 1986.

[13] A. ASToLFi, D. CHHABRA et R. ORTEGA : Asymptotic stabilization of some equilibria of an underactuated underwater vehicle. Systems Control Lett., 45(3):193206, 2002.

[14] Moussa BALDE et Ugo BoSCAiN : Stability of planar switched systems : the nondiagonalizable case. Commun. Pure Appl. Anal., 7(1):121, 2008.

[15] John M. BALL, Jerrold E. MARSDEN et Marshall SLEMRoD : Controllability for distributed bilinear systems. SIAM J. Control Optim., 20(4):575597, 1982.

[16] Werner BALLMANN, Mikhael GRoMov et Viktor SCHRoEDER : Manifolds of nonpositive curvature, volume 61 de Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, 1985.

[17] David BAo, Shiing-Shen CHERN et Zhongmin SHEN : An introduction to Riemann-Finsler geometry, volume 200 de Graduate Texts in Mathematics. Springer-Verlag, New York, 2000.

[18] Nikita E. BARABANov : An absolute characteristic exponent of a class of linear nonstationary systems of differential equations. Sibirsk. Mat. Zh., 29(4):12-22, 222, 1988.

[19] Nikita E. BARABANov : Asymptotic behavior of extremal solutions and structure of extremal norms of linear differential inclusions of order three. Linear Algebra Appl., 428(10):2357-2367, 2008.

[20] B. Ross BARMiSH : Stabilization of uncertain systems via linear control. IEEE Trans. Automat. Contr., 28(8):848-850, 1983.

[21] K. BEAuCHARD, Y. CHiTouR, D. KATES et R. LoNG : Spectral controllability for 2D and 3D linear Schrödinger equations. J. Funct. Anal., 256(12):3916-3976, 2009.

[22] Karine BEAuCHARD : Local controllability of a 1-D Schrödinger equation. J. Math. Pures Appl. (9), 84(7):851-956, 2005.

[23] Karine BEAuCHARD : Control of Schrödinger equations. Notes du Cours Peccot, Collège de France, 2007.

[24] Karine BEAuCHARD et Jean-Michel CoRoN : Controllability of a quantum particle in a moving potential well. J. Funct. Anal., 232(2):328-389, 2006.

[25] André BELLAICHE : The tangent space in sub-Riemannian geometry. In Sub-Riemannian geometry, volume 144 de Progr. Math., pages 1-78. Birkhäuser, Basel, 1996.

[26] H. C. BERG et R. ANDERSoN : Bacteria swim by rotating their flagellar filaments. Nature, 245:380-382, 1973.

[27] J. BLAKE : A finite model for ciliated micro-organisms. J. Biomech., 6:133-140, 1973.

[28] Franco BLANCHiNi et Stefano MiANi : Stabilization of LPV systems : state feedback, state estimation, and duality. SIAM J. Control Optim., 42(1):76-97, 2003.

[29] Anthony M. BLoCH, Roger W. BRoCKETT et Chitra RANGAN : The controllability of infinite quantum systems and closed subspace criteria. Preprint, 2006.

[30] Anthony M. BLoCH, Perinkulam Sambamurthy KRiSHNApRASAD, Jerrold E. MARSDEN et Gloria Sánchez de ALvAREz : Stabilization of rigid body dynamics by internal and external torques. Automatica J. IFAC, 28(4):745-756, 1992.

[31] Anthony M. BLoCH, Naomi Ehrich LEoNARD et Jerrold E. MARSDEN : Stabilization of mechanical systems using controlled Lagrangians. In Proceedings of the 36th IEEE Conference on Decision and Control, pages 2356-2361, 1997.

[32] Vincent D. BLoNDEL et Yurii NESTERov : Computationally efficient approximations of the joint spectral radius. SIAM J. Matrix Anal. Appl., 27(1):256272, 2005.

[33] Bernard BoNNARD, Jean-Baptiste CAiLLAu, Robert SiNCLAiR et Minoru TANAKA : Conjugate and cut loci of a two-sphere of revolution with application to optimal control. Ann. Inst. H. Poincaré Anal. Non Linéaire, 26(4):10811098, 2009.

[34] Ugo BoSCAiN : Stability of planar switched systems : the linear single input case. SIAM J. Control Optim., 41(1):89112, 2002.

[35] Ugo BoSCAiN, Thomas CHAMBRioN et Grégoire CHARLoT : Nonisotropic 3-level quantum systems : complete solutions for minimum time and minimum energy. Discrete Contin. Dyn. Syst. Ser. B, 5(4):957990, 2005.

[36] Ugo BoScAiN, Grégoire CHARLoT, Jean-Paul GAuTHiER, Stéphane GuERiN et Hans-Rudolf JAuSLiN : Optimal control in laser-induced population transfer for two- and three-level quantum systems. J. Math. Phys., 43(5):2107-2132, 2002.

[37] Ugo BoScAiN et Benedetto PiccoLi : A short introduction to optimal control. In T. SARi, éditeur : Contrôle Non Linéaire et Applications, pages 19-66. Hermann, Paris, 2005.

[38] Stephen BoyD, Laurent EL GHAoui, Eric FERoN et Venkataramanan BALAKRiSHNAN : Linear matrix inequalities in system and control theory, volume 15 de SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994.

[39] C. BRENNEN : An oscil lating-boundary-layer theory for ciliary propulsion. J. Fluid Mech., 65:799-824, 1974.

[40] Francesco BuLLo et Andrew D. LEwiS : Geometric control of mechanical systems, volume 49 de Texts in Applied Mathematics. Springer-Verlag, New York, 2005. Modeling, analysis, and design for simple mechanical control systems.

[41] Mark S. ByRD et Navin KHANEjA : Characterization of the positivity of the density matrix in terms of the coherence vector representation. Phys. Rev. A (3), 68(6):062322, 13, 2003.

[42] Thomas CHAMBRioN : Approximate tracking for a system of Schrödinger equations. Preprint, 2009.

[43] Stephen CHiLDRESS : Mechanics of swimming and flying, volume 2 de Cambridge Studies in Mathematical Biology. Cambridge University Press, Cambridge, 1981.

[44] Yacine CHiTouR : Applied and theoretical aspects of the controllability of nonholonomic control system. PhD Thesis, Rutgers University, 1996.

[45] Yacine CHiTouR, Jean-Michel CoRoN et Mauro GARAVELLo : On conditions that prevent steady-state controllability of certain linear partial differential equations. Discrete Contin. Dyn. Syst., 14(4):643-672, 2006.

[46] Monique CHyBA, Naomi Ehrich LEoNARD et Eduardo D. SoNTAG : Singular trajectories in multi-input time-optimal problems : application to controlled mechanical systems. J. Dynam. Control Systems, 9(1):103-129, 2003.

[47] Monique CHyBA, Helmut MAuRER, Héctor J. SuSSMANN et Vossen GoTTFRiED : Underwater vehicles : The minimum time problem. In Proceedings of the 43th IEEE Conference on Decision and Control, pages 1370-1375, 2004.

[48] Yves Colin de VERDiERE : Sur une hypothèse de transversalité d'Arnol'd. Comment. Math. Helv., 63(2):184-193, 1988.

[49] Jean-Michel CoRoN : Control and nonlinearity, volume 136 de Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2007.

[50] Jamal DAAFouZ et Jacques BERNuSSou : Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties. Systems Control Lett., 43(5):355359, 2001.

[51] René DAGER et Enrique ZuAZuA : Wave propagation, observation and control in 1-d flexible multi-structures, volume 50 de Mathématiques 6 Applications (Berlin) [Mathematics 6 Applications]. Springer-Verlag, Berlin, 2006.

[52] Domenico D'ALESSANDRo : Introduction to quantum control and dynamics. Applied Mathematics and Nonlinear Science Series. Boca Raton, FL : Chapman, Hall/CRC., 2008.

[53] Wijesuriya P. DAyAwANsA et C. F. MARTiN : A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Trans. Automat. Control, 44(4):751- 760, 1999.

[54] Lester E. DuBiNs : On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Amer. J. Math., 79:497- 516, 1957.

[55] Sylvain ERVEDozA et Jean-Pierre PuEL : Approximate controllability for a system of Schrödinger equations modeling a single trapped ion. Ann. Inst. H. Poincaré Anal. Non Linéaire, 26:2111-2136, 2009.

[56] Eric FERoN, Pierre APKARiAN et Pascal GAHiNET : Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions. IEEE Trans. Automat. Control, 41(7):1041-1046, 1996.

[57] Bruno FRANCHi et Ermanno LANCoNELLi : Une métrique associée à une classe d'opérateurs elliptiques dégénérés. Rend. Sem. Mat. Univ. Politec. Torino, (Special Issue):105-114 (1984), 1983. Conference on linear partial and pseudodifferential operators (Torino, 1982).

[58] D. FRENKEL et R. PoRTuGAL : Algebraic methods to compute Mathieu functions. J. Phys. A, 34(17):3541-3551, 2001.

[59] Giovanni P. GALDi : An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I, volume 38 de Springer Tracts in Natural Philosophy. Springer-Verlag, New York, 1994. Linearized steady problems.

[60] Jean-Paul GAuTHiER et Ivan A. K. KuPKA : Observability and observers for nonlinear systems. SIAM J. Control Optim., 32(4):975-994, 1994.

[61] José C. GERoMEL et Patrizio CoLANERi : Robust stability of time varying polytopic systems. Systems Control Lett., 55(1):81-85, 2006.

[62] V. V. GRuS'iN : A certain class of hypoelliptic operators. Mat. Sb. (N.S.), 83 (125):456-473, 1970.

[63] Alain HARAuX, Patrick MARTiNEz et Judith VANCosTENoBLE : Asymptotic stability for intermittently controlled second-order evolution equations. SIAM J. Control Optim., 43(6):2089-2108, 2005.

[64] Pascal HEBRARD et Antoine HENRoT : Optimal shape and position of the actuators for the stabilization of a string. Systems Control Lett., 48(3-4):199-209, 2003. Optimization and control of distributed systems.

[65] Dan HENRy : Perturbation of the boundary in boundary-value problems of partial differential equations, volume 318 de London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2005. With editorial assistance from Jack Hale and Antônio Luiz Pereira.

[66] Luc HiLLAiRET et Chris JuDGE : Generic spectral simplicity of polygons. Proc. Amer. Math. Soc., 137(6):21392145, 2009.

[67] Patrick HCHLER, Joachim BARGoN et Steffen J GLAsER : Nuclear magnetic resonance quantum computing exploiting the pure spin state of para hydrogen. J. Chem. Phys., 113(6):20562059, 2000.

[68] Velimir JuRDjEViC : Geometric control theory, volume 52 de Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1997.

[69] Tosio KATo : Perturbation theory for linear operators. Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer-Verlag New York, Inc., New York, 1966.

[70] Horace LAMB : Hydrodynamics. Cambridge Mathematical Library. Cambridge University Press, Cambridge, sixth édition, 1993. With a foreword by R. A. Caflisch [Russel E. Caflisch].

[71] Pier Domenico LAMBERTi et Massimo LANZA DE CRisToFoRis : Persistence of eigenvalues and multiplicity in the Dirichlet problem for the Laplace operator on nonsmooth domains. Math. Phys. Anal. Geom., 9(1):65-94, 2006.

[72] Naomi Ehrich LEoNARD : Mechanics and nonlinear control : Making underwater vehicles ride and glide. In Proc. 4th IFAC Nonlinear Control Design Symp., pages 1-6, 1998.

[73] Daniel LiBERZoN : Switching in systems and control. Systems & Control : Foundations & Applications. Birkhäuser Boston Inc., Boston, MA, 2003.

[74] James LiGHTHiLL : Mathematical biofluiddynamics. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. Based on the lecture course delivered to the Mathematical Biofluiddynamics Research Conference of the National Science Foundation held from July 16-20, 1973, at Rensselaer Polytechnic Institute, Troy, New York, Regional Conference Series in Applied Mathematics, No. 17.

[75] Jacques-Louis LioNs et Enrique ZuAZuA : A generic uniqueness result for the Stokes system and its control theoretical consequences. In Partial differential equations and applications, volume 177 de Lecture Notes in Pure and Appl. Math., pages 221-235. Dekker, New York, 1996.

[76] Daniela Lupo et Anna Maria MiCHELETTi : A remark on the structure of the set of perturbations which keep fixed the multiplicity of two eigenvalues. Rev. Mat. Apl., 16(2): 47-56, 1995.

[77] Michael MARGALioT et Christos YFouLis : Absolute stability of third-order systems : a numerical algorithm. Automatica J. IFAC, 42(10):1705-1711, 2006.

[78] Paolo MAsoN, Ugo BosCAiN et Yacine CHiTouR : Common polynomial Lyapunov functions for linear switched systems. SIAM journal on control and optimization, 45:226-245, 2006.

[79] T.A. MEYNARD, H. FoCH, P. THoMAs, J. CouRAuLT, R. JAkoB et M. NAHRsTAEDT : Multicell converters : basic concepts and industry applications. IEEE Transactions on Industrial Electronics, 49(5):955-964, 2002.

[80] Anna Maria MiCHELETTi : Perturbazione dello spettro dell'operatore di Laplace, in relazione ad una variazione del campo. Ann. Scuola Norm. Sup. Pisa (3), 26:151-169, 1972.

[81] Mazyar MiRRAHiMi : Lyapunov control of a particle in a finite quantum potential well. In Proceedings of the 45th IEEE Conference on Decision and Control, 2006.

[82] Mazyar MiRRAHiMi : Lyapunov control of a quantum particle in a decaying potential. Ann. Inst. H. Poincaré Anal. Non Linéaire, 26(5):1743-1765, 2009.

[83] Mazyar MiRRAHiMi et Pierre RouCHoN : Controllability of quantum harmonic oscillators. IEEE Trans. Automat. Control, 49(5):745747, 2004.

[84] Dirk MiTTENHuBER : Dubins' problem in the hyperbolic plane using the open disc model. In Geometric control and non-holonomic mechanics (Mexico City, 1996), volume 25 de CMS Conf. Proc., pages 115152. Amer. Math. Soc., Providence, RI, 1998.

[85] Dirk MiTTENHuBER : Dubins' problem is intrinsically three-dimensional. ESAIM Control Optim. Calc. Var., 3:122, 1998.

[86] Felipe MoNRoY-PEREZ : Three-dimensional non-Euclidean Dubins' problem. In Geometric control and non-holonomic mechanics (Mexico City, 1996), volume 25 de CMS Conf. Proc., pages 153181. Amer. Math. Soc., Providence, RI, 1998.

[87] Vahagn NERsEsyAn : Growth of Sobolev norms and controllability of the Schrödinger equation. Comm. Math. Phys., 290(1):371-387, 2009.

[88] S. P. Novikov et I. ShmEL'tsER : Periodic solutions of Kirchhoff equations for the free motion of a rigid body in a fluid and the extended Lyusternik-Shnirel'man-Morse theory. I. Funktsional. Anal. i Prilozhen., 15(3):54-66, 1981.

[89] Jaime H. ORtEgA et Enrique ZuAzuA : Generic simplicity of the spectrum and stabilization for a plate equation. SIAM J. Control Optim., 39(5):1585-1614, 2000.

[90] Jaime H. ORtEgA et Enrique ZuAzuA : Generic simplicity of the eigenvalues of the Stokes system in two space dimensions. Adv. Differential Equations, 6(8):987-1023, 2001.

[91] A PEiRcE, M DAhLEh et H RAbitz : Optimal control of quantum mechanical systems: Existence, numerical approximations, and applications. Phys. Rev. A, 37:4950-4964, 1988.

[92] Fernand PELLEtiER : Sur le théorème de Gauss-Bonnet pour les pseudo-métriques singulières. In Séminaire de Théorie Spectrale et Géométrie, No. 5, Année 1986-1987, pages 99-105. Univ. Grenoble I, Saint, 1987.

[93] V. Yu. PRotAsov : A generalized joint spectral radius. A geometric approach. Izv. Ross. Akad. Nauk Ser. Mat., 61(5):99-136, 1997.

[94] E. M. PuRcELL : Life at low Raynolds numbers. Am. J. Phys., 45:3-11, 1977.

[95] H. RAbitz, H. de ViviE-RiEdLE, R. Motzkus et K. KompA : Wither the future of controlling quantum phenomena? SCIENCE, 288:824-828, 2000.

[96] Rajamani RAvi, Krishan M. NAgpAL et Pramod P. KhARgonEkAR : H8 control of linear time-varying systems : a state-space approach. SIAM J. Control Optim., 29(6):1394-1413, 1991.

[97] Michael REEd et Barry Simon : Methods of modern mathematical physics. IV. Analysis of operators. Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1978.

[98] Franz RELLich : Perturbation theory of eigenvalue problems. Assisted by J. Berkowitz. With a preface by Jacob T. Schwartz. Gordon and Breach Science Publishers, New York, 1969.

[99] Sérgio S. RodRiguEs : Navier-Stokes equation on the rectangle controllability by means of low mode forcing. J. Dyn. Control Syst., 12(4):517-562, 2006.

[100] Pierre Rouchon : Control of a quantum particle in a moving potential well. In Lagrangian and Hamiltonian methods for nonlinear control 2003, pages 287-290. IFAC, Laxenburg, 2003.

[101] Jorge SAn MARtín, Takéo TAkAhAshi et Marius TucsnAk : A control theoretic approach to the swimming of microscopic organisms. Quart. Appl. Math., 65:405-424, 2007.

[102] T. SEidEmAn et E. HAmiLton : Nonadiabatic alignment by intense pulses : concepts, theory and directions. Adv. At. Mol. Opt. Phys., 52:289, 2006.

[103] M. ShApiRo et P. BRumER : Principles of the Quantum Control of Molecular Processes. Principles of the Quantum Control of Molecular Processes, pp. 250. Wiley-VCH, février 2003.

[104] Takashi ShioyA : The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature. Trans. Amer. Math. Soc., 351(5):17651801, 1999.

[105] M. SpAnnER, E. A. ShApiRo et M. IvAnov : Coherent control of rotational wave-packet dynamics via fractional revivals. Phys. Rev. Lett., 92:093001, 2004.

[106] Michael SpivAk : A comprehensive introduction to differential geometry. Vol. II. Publish or Perish Inc., Wilmington, Del., second édition, 1979.

[107] H. STApELFELDT et T. SEiDEMAN : Aligning molecules with strong laser pulses. Rev. Mod. Phys., 75:543, 2003.

[108] D. SUGNy, A. KELLER, O. ATABEK, D. DAEMS, C. DioN, S. GUERiN et H. R. JAUSLiN : Reaching optimally oriented molecular states by laser kicks. Phys. Rev. A, 69:033402, 2004.

[109] H. J. SUSSMANN et G. TANG : Shortest paths for the Reeds-Shepp car : a worked out example of the use of geometric techniques in nonlinear optimal control. Rutgers Center for Systems and Control Technical Report 91-10, 1991.

[110] Héctor J. SUSSMANN : Shortest 3-dimensional paths with a prescribed curvature bound. In Proceedings of the 34th IEEE Conference on Decision and Control, 1995.

[111] G. TAyLoR : Analysis of the swimming of microscopic organisms. Proc. Roy. Soc. London. Ser. A., 209:447-461, 1951.

[112] Stefan TEUFEL : Adiabatic perturbation theory in quantum dynamics, volume 1821 de Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2003.

[113] Mikhail TEyTEL : How rare are multiple eigenvalues? Comm. Pure Appl. Math., 52(8): 917-934, 1999.

[114] Gabriel TURiNici : On the controllability of bilinear quantum systems. In M. DEFRANcEScHi et C. LE BRiS, éditeurs : Mathematical models and methods for ab initio Quantum Chemistry, volume 74 de Lecture Notes in Chemistry. Springer, 2000.

[115] Karen UHLENBEcK : Eigenfunctions of Laplace operators. Bull. Amer. Math. Soc., 78: 1073-1076, 1972.

[116] Enrique ZUAzUA : Switching controls. Journal of the European Mathematical Society, à paraître.

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