Marc Quincampoix

Books

  • Advances in Dynamic Games Theory, S. Jorgensen, M. Quincampoix, T. Vincent Editors, in `` Annals of International Society of Dynamic Games'' , Birkhauser 2007.
  • Differential games, M. Quincampoix, in `` Encyclopedia of Complexity and System Science, '' Springer 2008.

    • Research Papers

    Published (or about to be) articles:
    1. The problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures (with O. Serea ) in `` Nonlinear Analysis ''Nonlinear Analysis TMA Volume 72, Issue 6, Pages 2803-2815 (2010)
    2. Another proof for the equivalence between invariance of closed sets with respect to stochastic and deterministic systems (with Buckdahn R., Rainer C. and Teichman J. ) in `` Bulletin des Sciences Mathématiques '' Vol 134 pp. 207-214 (2010) (Available online 24 November 2007)
    3. Existence of Equilibria of Set-valued Maps on Bounded Epilipschitz Domains in Hilbert Spaces without Invariance Conditions (with A. Goudovitch, M. Kamenskii ) in `` Nonlinear Analysis ''Nonlinear Analysis TMA Volume 72, Issue 1, Pages 262-276 (2010)
    4. On limiting values of stochastic differential equations with small noise intensity tending to zero (with Buckdahn R. and Ouknine Y. ) in `` Bulletin des Sciences Mathématiques ''Bull. Sci. math. 133 (2009) 229–237
    5. Linear programming analysis of deterministic infinite horizon optimal control problems (discounting and time averaging cases) (with V. Gaitsgory )
      6. in `` SIAM Journal of Control and Opti. '' Vol. 48, 4, pp. 2480-2512 (2009)
    6. Existence of periodic solutions of a ordinary differential equation perturbed by a small parameter: An averaging approach (with A. Gudovich and M. Kamenski ) in `` Comptes rendus mathématiques de l'Académie des Sciences, Paris. '' C. R. Acad. Sci. Paris, Ser. I 347 (2009) 369–374
    7. Parameterized minimax problem: on Lipschitz-like dependence of the solution with respect to the parameter (with N. Zlateva )
      8. in `` SIAM J. Optim. '' Vol. 19, N. 3, pp. 1250-1269 (2008)
    8. Deterministic differential games under probability knowledge of initial condition (with P. Cardaliaguet )
      9. in ``International Game Theory Review '' Vol. 10, N. 1, 1-16 (2008).
    9. Controlled Stochastic Differential Equations under constraints in infinite dimensional spaces (with R. Buckdahn and G. Tessitore )
      10. in `` SIAM Journal of Control and Opti. '' Vol. 47, 1, 218-250 (2008).
    10. On the reachability problem for uncertain Hybrid Systems (with Gao Y. and Lygeros J. ) in `` IEEE Transaction on Automatic Control '' Vol. 52, N. 9, 1572-1587 (2007).
    11. An Averaging method for singularly perturbed systems with Hysteresis in Infinite Dimensional Spaces (with Goudovitch A., Kamenskii M. Nistri P.)in `` Differential Equations and Dynamical systems'' Vol. 15, N.3-4, pp. 267-294 (2007) .
    12. Impulse Differential Inclusions Driven by Discrete Measures (with Lygeros J. and Rzezuchowski T. ) in `` Lecture Notes in Computer Science '' Springer, Vol. 4416/2007, pp. 385-398. (2007).
    13. Pursuit Evasion games with impulsive Dynamics (with Cruck E. and Saint-Pierre P.) in Annals of International Society of Dynamic Games, Birkhauser Vol. 9, pp. 223-248, (2007).
    14. Zero-sum state constrained differential games: Existence of value for Bolza problem. (with P. Bettiol and P. Cardaliaguet ) in `` International Journal of Game Theory'' Vol. 34, N.4, pp. 495-527. (2006)
    15. On Lipschitz Regularity of Minimizers of a Calculus of Variations Problem with non Locally Bounded Lagrangians (with N. Zlateva ) in in `` Comptes rendus Mathématiques,'' Vol. 343, 1, Pages 69-74 (2006).
    16. Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality (with M. Forti and P. Nistri)in `` IEEE Transactions on Neural networks '' Vol. 17 , No. 6, pp.1471-1486 (2006).
    17. Aubin Criterion for Metric Regularity, (with A. Dontchev and N. Zlateva) in `` Journal of convex Analysis ''Vol. 13 , No. 2, pp 281-297 (2006).
    18. The Reachability Problem for Uncertain Hybrid Systems Revisited: A Viability Theory Perspective (with Y. Gao and J. Lygeros ) in `` Lecture Notes in Computer Science, Springer,'' Volume 3927, pp. 242 - 256 (2006)
    19. A characterization of approximately controllable linear stochastic differential equation (with R. Buckdahn and G. Tessitore ) in `` Stochastic Partial differential Equations and Applications, G. Da Prato and L. Tubaro Eds '' Series of Lecture Notes in pure and appl. Math., Chapman & Hall Vol.245 , pp. 253-260 (2006)
    20. Existence of Equilibria on Epilipschitz sets without invariance conditions (with M. Kamenskii ) in `` Fixed Point Theory and Applications '' Vol.2005 , N. 3, pp. 257-279 (2005)
    21. Stochastic control and compatible subsets of contraints (with C. Rainer ) in `` Bulletin des Sciences Mathématiques '' Vol.129, N. 1, pp. 39-55 (2005).
    22. Optimal Control of Uncertain Systems with Incomplete Information for the Disturbances, (with V. Veliov ) in `` SIAM J. Control and Optimization '' Vol.43 N. 4. pp.1373-1399 (2005)
    23. On the Dynamics of a Differential Inclusion built upon a Nonconvex Constrained Minimization Problem . (with P. Nistri) in `` J. Optimization Theory and Appl. '' Vol. 129, N. 1 pp.39-55. (2005).
    24. On attainability of a set by at least one solution to a differential inclusion, (with G. Gabor ) in `` Optimization,'' vol.53, N.5-6 pp.563-582 (2004)
    25. On the Control of Uncertain Impulsive Systems: Approximate Stabilization and Controlled Invariance (with Gao, Y. Lygeros J. Seube N.) in `` International Journal of Control '' Vol. 77, N. 16, pp.1393-1407 (2004). .
    26. Averaging of Perturbed One-Sided-Lipschitz Differential Inclusions , (with T. Donchev and M. Kamenskii ) in `` Zeitschrift fur Analysis und ihre Anwendungen '' Vol. 23, N. 4, pp 1-10 (2004).
    27. A Two-point Boundary Value Problem for a class of Differential Inclusions, (with T. Donchev ) in `` Journal of Convex and Nonlinear Analysis ''Vol. 5, N. 1, pp. 59-70 (2004)
    28. Stochastic Control with Exit Time and Constraints, Application to Small Time Attainability of sets (with R. Buckdahn, C. Rainer A. Rascanu) in `` Appl. Math. Optim.'' Vol. 49, 2, pp.99-112. (2004)
    29. Generalized Neural Network for Non-Smooth Programming Problems, (with M. Forti and P. Nistri) in `` IEEE Transactions on Circuit and Systems'' Vol. 51, 9, pp.1741-1753. (2004)
    30. Averaging method for discontinuous Mayer's problem of singularly perturbed control systems (with F. Wattbled) in `` Nonlinear Analysis: Theory, Methods \& Applications ''Vol. 54, pp. 819-837 (2003) .
    31. Approximate stabilisation of uncertain hybrid systems (with Gao, Y. Lygeros J. Seube N.) in `` Proceedings of Computation and control. 6th international workshop, HSCC 2003, Berlin: Springer. Lect. Notes Comput. Sci. '', 2623, pp. 203-215,(2003) .
    32. Equilibria and strict equilibria of multivalued maps on noninvariant sets (with G. Gabor and P. Cardaliaguet) in `` Annales Polonici Mathematici, '', vol 82-1, pp.19-37, (2003) .
    33. On Nonemptiness of viability kernels for infinite-dimensional differential inclusions (with T. Donchev) in `` Applied Maths Letters. '', Vol. 16, pp 1195-1199 (2003).
    34. On Existence of Equilibria of Lipschitz Set-Valued Maps (with G. Gabor) in Bolletino Unione Math. Italian. '', 8, 6-B, pp.309-321 (2003).
    35. On Existence of Solutions to Differential Equations or Inclusions Remaining in a Prescribed Closed Subset of a Finite-dimensional Space . (with G. Gabor ) in `` J. Differential Equations '' Vol. 185, No. 2, pp. 483-512 (2002).
    36. Singularly perturbed second order differential inclusions by an averaging method. . (with M. Kamenskii, P. Nistri) in `` International Journal of Pure and Applied Mathematics '' vol. 3, N. 3, pp. 343-355 (2002).
    37. A representation formula for the mean curvature motion (with R. Buckdahn and P. Cardaliaguet), in ``SIAM J. Math. Anal." Vol. 33, N. 4, pp.827-846.(2002)
    38. Oleinik-Lax formulas and multitime Hamilton-Jacobi systems (with S. Plaskacz) in `` Nonlinear Analysis: Theory, Methods \& Applications ''Vol. 51, N. 6 pp. 957-967 (2002) .
    39. Optimal control in presence of unobservable uncertainties (with V. Veliov ) in `` Proceedings of Bulgarian Academy of Sciences '' T. 55, N. 8 pp.11-16 (2002).
    40. Viability of moving sets for stochastic differential equations (with Buckdahn R. ,Rainer C. , A. Rascanu) in `` Advances in differential Equations '' Vol. 7, N. 9, pp. 1045--1072 (2002).
    41. Optimal control of discrete-time uncertain systems with imperfect measurement (with R. Moitié, V. Veliov) in `` IEEE transactions on Automatic Control''Vol. 47, 11, pp. 1909-1914. (2002).
    42. On open-loop and feedback attainability of a closed set for nonlinear control systems . (with P. Nistri) in `` J. Math. Anal. Appl '' Vol. 270, No. 2, pp. 474-487, (2002).
    43. A Viability Approach for Optimal Control with Infimum Cost, (with O. Serea ) in `` Annals. Stiint. Univ. Al. I. Cuza Iasi,s.I a, Mat, '' t. XLVIII, f.1., p. 113 - 132 (2002).
    44. Solutions Tubes for Differential Inclusions within a Collection of sets. (with V. Veliov ) in `` Control and Cybernetics. Vol 31. 3, pp.849-862. '' (2002).
    45. Differential games with state-constraints . (with P. Cardaliaguet and P. Saint-Pierre ) in `` Petrosjan, L. A. (ed.) et al., 10th international symposium on dynamic games and applications. St. Petersburg, Russia. In 2 vol. St. Petersburg: International Society of Dynamic Games, St. Petersburg State Univ. '' pp.179-182. (2002)
    46. Impulse differential inclusions: A viability approach to hybrid systems (with Aubin J-P. Lygeros J.\ Sastry S. Seube N.) in `` IEEE transactions on Automatic Control'' vol. 47, 1, pp. 2-20, 2002.
    47. Representation formulas for Hamilton Jacobi equations related to calculus of variation problems. (with S. Plaskacz) in `` Topological Methods in Nonlinear Analysis, '' vol. 20, pp.85-118, 2002.
    48. De l'existence de solutions d'équations différentielles assujetties à rester dans un ensemble fermé. . (with G. Gabor ) in `` Comptes-Rendus de l'Acad\'emie des Sciences. S\'erie I. PARIS, vol 333, pp. 913-918 '' (2001).
    49. Sliding mode control of uncertain systems: a singular perturbation approach . (with M. Kamenskii, P. Nistri) in `` IMA J. Math. Control, '' 19, 4, pp. 377-398 (2002).
    50. Value-functions for differential games and control systems with discontinuous terminal cost. (with S. Plaskacz) in `` SIAM J. Control and Optimization '' Vol. 39, N. 5 (2001),  pp. 1485-1498 1615-1632.
    51. Local small time controlability and attainability of a set for nonlinear control system. (with M.Krastanov) in `` ESAIM Control, Opti and Calcul. of Variations, '' Vol. 6, pp. 499-516.(2001)
    52. Pursuit differential games with state constraints. (with P. Cardaliaguet and P. Saint-Pierre) in `` SIAM J. Control and Optimization '' Vol. 39, N. 5 (2001),  pp.1615-1632
    53. Discontinuous Mayer control problem under state-constraints. (with S. Plaskacz) in `` Topological Methods in Nonlinear Analysis, '' Vol 15, pp. 91-100.(2000).
    54. Numerical schemes for discontinuous value functions of optimal control (with P. Cardaliaguet and P. Saint-Pierre) in `` Set-valued Analysis '' Vol. 8, N. 1 & 2 (2000) pp: 111-126.
    55. Stochastic Viability For Backward Stochastic Differential Equations and Applications to Partial Differential Equations. (with Buckdahn R. , A. Rascanu) in `` Probability Theory and Relat. fields '' .Vol. 116, pp. 485-504.(2000)
    56. Dissipative control systems and disturbance attenuation for nonlinear-H infty control problems. (with H. Frankowska) in `` Appl. Math. Optim.''vol. 40 N. 2 pp 163-181. (1999).
    57. Numerical methods for differential games. (with P. Cardaliaguet and P. Saint-Pierre) in `` Stochastic and differential games : Theory and numerical methods '' (1999) pp. 177-247. Annals of the international Society of Dynamic Games, M. Bardi, T.E.S. Raghavan, T. Parthasarathy Eds. Birkhauser.
    58. Viability under uncertain initial state (with V. Veliov) in `` Set-valued Analysis ''.ol. 7 No 1, pp. 55-87.1999
    59. Singular Perturbations for differential equations and inclusions : an Approach through constrained Systems. in `` Nonlinear Analysis: Theory, Methods \& Applications '' Vol. 32, N.5, pp.697-710.1998.
    60. Existence of stochastic control under state constraints. (with Buckdahn R. Peng S., Rainer C. ) in `` Comptes-Rendus de l'Académie des Sciences. Série I.'' PARIS, t. 327, pp. 17-22. (1998).
    61. Stabilization of uncertain Control Systems through Piecewise Constant Feedback. . (with S.Seube) in `` J. Math. Anal. Appl '' N. 196 pp.240-255.1998.
    62. On a generalization of Tichonoff Theorem to Differential Inclusions . in `` Doklady of Russian Academy of Sciences (in russian) '' V.360, N. 3, 1998, PP.309-312.
    63. An Algorithm for Viability Kernels in Holderian Case:Approximation by discrete dynamical systems. (with P. Saint-Pierre) in `` J. Mathematics of Systems, Estimation and Control. Mat.'' Vol, 8,N.1,pp.17-29.1998
    64. Multitarget Control Problems. (with L. Doyen) in ``J. Optimization Theory and Applt .'' vol.93, pp.121-140. 1997
    65. Propriétés de Viabilité pour des équations différentielles stochastiques rétrogrades et applications à des équations aux dérivées partielles. (with Buckdahn R.,, Rascanu A. ) in `` Comptes-Rendus de l'Académie des Sciences. S\'erie I. PARIS, '' t. 325, pp. 1159-1162.(1997).
    66. Optimal times for constrained nonlinear control problems without local controllability. (with P. Cardaliaguet and P. Saint-Pierre) in `` Appl. Math. Opti.'' Vol. 36 (1997) pp: 21-42.
    67. Singular perturbations in nonlinear optimal control. (with H. Zhang) in ``Differential and Integral Equations, .'' Vol. 8, N.4,pp.931-944.1995
    68. Contribution à l'étude des jeux différentiels quantitatifs et qualitatifs avec contrainte sur l'état. (with P. Cardaliaguet and P. Saint-Pierre), in `` Comptes-Rendus de l'Académie des Sciences. Série I. PARIS, '' t. 321, pp. 1443-1548.(1995).
    69. Some Algorithms for Differential Games with two Players and one Target (with P. Cardaliaguet and P. Saint-Pierre), in `` RAIRO Mathematical Modeling and Numerical Analysis '', .Vol 28, N,4.pp. 441-461. (1994)
    70. Temps optimaux pour des problèmes de contrôle avec contraintes et sans contrôlabilité locale. (with P. Cardaliaguet and P. Saint-Pierre), in `` Comptes-Rendus de l'Académie des Sciences. Série I. PARIS, '' t. 318, pp.607-612 (1994).
    71. Perturbations singulières pour des problèmes de contrôles et des inclusions différentielles. in `` Comptes-Rendus de l'Académie des Sciences. Série I. PARIS, t. 318, pp.607-612'' (1993).
    72. Differential inclusions and target problems in `` SIAM J. Control and Optimization '' Vol. 30, No 2, pp.324-335. 1992
    73. Enveloppes d'invariance pour des inclusions différentielles Lipschitziennes: Application aux problèmes de cibles. in `` Comptes-Rendus de l'Académie des Sciences. Série I.'' PARIS, t.314, pp.343-347.1992
    74. Un algorithme déterminant les noyaux de viabilité pour les inclusions différentielles avec contraintes (with H. Frankowska) in `` Comptes-Rendus de l'Académie des Sciences. S\'erie I. PARIS,'' t. 312, pp. 31-36. 1991
    75. Viability kernels of differential inclusions with constraints: Algorithm and applications. (with H. Frankowska) in `` J. Mathematics of Systems, Estimation and Control. Mat.'' vol.1, No 3, pp.371-388.,1991
    76. Playable Differential Games . in `` J. Math. Anal. Appl '' vol.1, No 1, pp. 194-211.1991.
    77. Frontières de domaines d'invariance et de viabilité pour des inclusions différentielles avec contraintes. in `` Comptes-Rendus de l'Académie des Sciences. Série I. PARIS, t. 311, pp. 904-914. 1991


    Preprints:

    1. Holder Metric Regularity of Set-Valued Maps (with H. Frankowska )
    2. On Existence of a limit value in some non expansive optimal control problems (with J. Renault)
    3. Regularity Properties of a Class of Fully Nonlinear Parabolic Equations (with R. Buckdahn and P. Cannarsa)
    4. Optimal Control with Hysteresis Nonlinearity and Multidimensional Play Operator (with A. Gudovich)
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