Pierre BERNHARD

Directeur de recherches émérite
Projet BIOCORE
INRIA-Sophia Antipolis-Méditerranée

Pierre.Bernhard@inria.fr

Tel : +33 (0)4 97 15 53 87

Officier de l’ordre national du mérite
Chevalier de la Légion d’Honneur
Prix Michel Monpetit de l’Académie des Sciences

J’ai été ...

- Professeur (Automatique) à l’École Nationale Supérieure des Mines de Paris (ENSMP), 1970 – 1976
- Professeur (Mathématiques) à l’université Paris 9 Dauphine, 1976 – 1981
- Directeur du Centre d’Automatique et Informatique de l’ENSMP, 1972 – 1981
- Directeur, INRIA-Sophia Antipolis, 1981 – 1996
- Professeur (Mathématiques) à l’université de Nice-Sophia Antipolis (UNS) 1996 – 2008
- Directeur d’I3S, unité mixte UNS – CNRS, 2000 – 2004


Mes Travaux ...

sont tous plus où moins liés à la théorie des jeux dynamiques et leurs applications, autrefois aux modèles de combat, la commande robuste et H-infini-optimale, la finance, l’économie, aujourd’hui principalement à la biologie mathématique : écologie comportementale, biologie évolutive, jeux évolutionnaires, dynamique des populations.

Je suis fier d’avoir reçu en 2008 l’Isaacs Award de l’International Society of Dynamic Games.

Publications

[70.1] Linear Differential Games and the Isotropic Rocket. PhD dissertation, Stanford University, SUDAAR 413. 1970.

[72.1] Pierre Bernhard. Sur la commandabilité des systèmes linéaires discrets à deux joueurs. RAIRO J3, pp 53-68, 1972.

[72.2] Pierre Bernhard. Conditions de raccordements pour les jeux différentiels. 5th IFAC World Congress, Paris, 1972.

[72.3] Pierre Bernhard. Introduction a la Teoria del Control Optimo. (143 p.) Cuadernos del Istituto de Matematica Beppo Levi, Rosario, Argentina. 1972.

[73.1] Pierre Bernhard et Guy Cohen. Étude d'une fonction fréquentielle intervenant dans un problème de commande optimale, avec une application à la réduction de la taille de ce problème. RAIRO J2, pp 63-85, 1973.

[73.2] Pierre Bernhard and Gilles Bellec. On the evaluation of worst case design, with an application to the linear quadratic synthesis technique. 3rd IFAC Symposium on Sensitivity, Adaptivity and Optimality, Ischia, Italy, 1973.

[74.1] Pierre Bernhard and Guy Cohen. Complete dependence of the optimal control problem. Ricerche di Automatica 5, pp 1-15, 1974.

[74.2] Pierre Bernhard, Albert Benveniste, Guy Cohen and Jean Chatelon. A new algorithm for gauss-Markov identification. IFIP Technical Conference on Optimization Techniques, Novosibirsk, USSR, 1974.

[75.1] Pierre Bernhard. New Results about Corners in Differential Games Including State Constraints. 6th IFAC World Congress, Boston, 1975.

[75.2] Pierre Bernhard. Le filtrage statistique. Annales des Mines Novembre 1975, pp 11-18.

[75.3] Pierre Bernhard and Jean-François Abramatic. Contraintes d'État dans les jeux différentiels. In Control Theory, Numerical Methods and Computers Systems Modelling, Springer. pp 119-133. 1975.

[76.1] Albert Benveniste, Guy Cohen and Pierre Bernhard. On the decomposition of stochastic control problems. 1st IFAC Symposium on Large Scale Systems Theory and Applications. Udine, Italy, 1976.

[76.2] Pierre Bernhard. Commande optimale, Décentralisation et Jeux Dynamiques. Dunod, Paris, 1976.

[77.1] Pierre Bernhard. Singular surfaces in differential games, an introduction. In P. Haggedorn, G-J. Olsder and H. Knobloch: Differential Games and Applications. Springer Lecture Notes in Control and Information Sciences 3, pp 1-33, 1977.

[79.1] Pierre Bernhard. Linear quadratic zero-sum two-person differential games: necessary and sufficient condition. JOTA 27, pp 51-69 and 31, pp 283-284, 1979.

[79.2] Pierre Bernhard. Contribution à l'étude des jeux différentiels à deux joueurs, somme nulle et information parfaite. Thèse de doctorat d'État, Université Paris 6, (347 p.) 1979.

[80.1] Pierre Bernhard. Exact controlabibility of perturbed continuous time linear systems. IEEE Transactions on Automatic Control AC 25, pp 89-96, 1980.

[80.2] Guy Cohen et Pierre Bernhard. L'histoire des quatre automobilistes au pays imaginaire, ou comment se comporter face à l'incertain. Informatique et Gestion 115, pp 71-76. 1980.

[80.3] Pierre Bernhard. Théorie des systèmes et jeux différentiels. Économie et Société XIV, pp 1311-1336, 1980.

[81.1] Pierre Bernhard. Un aperçu de la théorie des jeux différentiels. RAIRO J15, pp279-302. 1981.

[81.2] Pierre Bernhard. From classical to modern signal processing: some aspects of the theory. In J-P. Aubin, A. Bensoussan and I. Ekeland eds. Mathematical Techniques of Optimization, Control, and Decision, Birkhaüser. pp 131-150. 1981

[82.1] Pierre Bernhard. On singular implicit linear dynamical systems. SIAM Journal on Control and Optimization 20, pp 612-633. 1982.

[82.2] Pierre Bernhard et Gregory Tomski. Une contruction rétrograde dans les jeux différentiels qualitatifs et application à la régulation. RAIRO J16, pp71-84. 1982.

[83.1] Pierre Bernhard. Automatique. Encyclopaedia Universalis. 1983.

[86.1] Pierre Bernhard, Anne-Laure Colomb and George Papavassilopoulos. Rabbit and hunter game : two discrete stochastic formulations. Computers and Mathematics with Applications 13, pp 205-225. 1986.

[86.2] Xiao-Min Wang, Pierre Bernhard and José Grimm. Commande optimale linéaire quadratique des systèmes implicites discrets. Compte rendu à l'Acadéie des Sciences, Série I, 303, pp127-130.

[87.1] Pierre Bernhard. Differential Games: Introduction. pp 1009-1010. In Madan G, Singh ed. Systems and Control Encyclopaedia, Pergamon Press, 1987.

[87.2] Pierre Bernhard. Differential Games: Open Loop. pp 1020-1024. In Madan G, Singh ed. Systems and Control Encyclopaedia, Pergamon Press, 1987.

[87.3] Pierre Bernhard. Differential Games: Closed Loop. pp 1004-1009. In Madan G, Singh ed. Systems and Control Encyclopaedia, Pergamon Press, 1987.

[87.4] Pierre Bernhard. Differential Games: Isaacs Equation. pp 1010-1016. In Madan G, Singh ed. Systems and Control Encyclopaedia, Pergamon Press, 1987.

[87.5] Pierre Bernhard. Differential Games: Linear Quadratic. pp 1017-1020. In Madan G, Singh ed. Systems and Control Encyclopaedia, Pergamon Press, 1987.

[87.6] Pierre Bernhard. Differential Games: Riccati Equations and Conjugate Points. pp 1017-1020. In Madan G, Singh ed. Systems and Control Encyclopaedia, Pergamon Press, 1987.

[87.7] Pierre Bernhard. Differential Games: Linear Quadratic Regulator Problem. pp 1017-1020. In Madan G, Singh ed. Systems and Control Encyclopaedia, Pergamon Press, 1987.

[87.8] Pierre Bernhard et Xiao-Min Wang. Filtrage des systèmes implicites discrets. Compte rendu à l'Académie des Sciences, Série I, 304, pp 351-354, 1987.

[87.9] Pierre Bernhard. Computation of equilibrium points of delayed, partial information, pursuit-evasion games. 26th IEEE Conference on Decision and Control, Los Angeles, 1987.

[88.1] Pierre Bernhard and Annie-Laure Colomb. Saddle point conditions for a class of stochastic differential games with imperfect information. IEEE Transactions on Automatic Control AC 33, pp 89-101, 1988.

[89.1] Pierre Bernhard, José Grimm and Xiao-Min Wang. Basic system theory for singular implicit systems. IFAC Workshop on System Structure and Control: State Space and Polynomial Methods. Prague, 1989.

[89.2] Tamer Başar and Pierre Bernhard. (editors) Differential Games and Applications. Springer Lecture Notes in Control and Information Sciences 119, 1989.

[90.1] Pierre Bernhard and Josef Shinar. On finite approximations of a game solution with mixed strategies. Applied Mathematics Letters 3, pp 1-4, 1990.

[90.2] John Breakwell and Pierre Bernhard. A simple game with a singlar focal line. Journal of Optimization Theory and Applications 64, pp 419-428. 1990.

[90.3] Pierre Bernhard, Jean-Marie Nicolas and Vincent Laporte. About the resolution of discrete pursuit games and its applications to naval warfare. 4th ISDG International Symposium on Dynamical Games and Applications. Helsinki, Finland, 1990.

[90.4] Pierre Bernhard, José Grimm et Xiao-Min Wang. Commande optimale linéaire quadratique des systèmes implicites discrets. APII 24, pp 17--36. 1990.

[91.1] Tamer Başar and Pierre Bernhard. H-infinity-Optimal Control and related Minimax Design Problems (1st edition.) Birkhaüser, 1991. (See 2nd edition: [95.5])

[91.2] Pierre Bernhard. Application of the min-max certainty equivalence principle to the sampled data output feedback H-infinity control problem. Systems and Control Letters 16, pp 229-234, 1991.

[91.3] Xiao-Min Wang et Pierre Bernhard. Filtrage et lissage des systèmes implicites discrets. APII 25, pp 205-228. 1991.

[91.4] Pierre Bernhard and Bernard Larrouturou. Étude de la barrière pour un problème de fuite optimale dans le plan. APII 25, pp 205-228. 1991.

[91.5] Pierre Bernhard and Odile Pourtallier. Rabbit and hunter : a partial information game. International conference on game theory. Florence, Italy, 1991.

[92.1] Pierre Bernhard. Information and strategies in dynamic games. SIAM Journal on Control and Optimization, 30, pp 212-228, 1992.

[92.2] Laurent Baratchart and Pierre Bernhard. Automatique et systèmes. Les Techniques de l'Ingéneur, pp 1-27, 1992

[92.3] Pierre Bernhard, Jean-Marie Nicolas and Odile Pourtallier. Pursuit games with costly information, two approaches. 5th ISDG international symposium, Grimentz, Switzerland, 1992.

[92.4] Alain Bensoussan and Pierre Bernhard. Remarks on the theory of robust control. In Optimization, Optimal Control, and Partial Differential Equations, Birkhaüser International Series in Numerical Mathematics, 107, pp 149-166, 1992.

[93.1] Alain Bensoussan and Pierre Bernhard. On the standard problem of H-infinity-optimal control for infinite dimensional systems. In Identification and Control of Systems Governed by Patial Differential Equations, (South Hadley, Ma, 1992), pp 117-140, SIAM, 1993.

[93.2] Garry Didinsky, Tamer Başar, and Pierre Bernhard. Structural properties of minimax policies for a class of differential games arising in nonlinear H-infty-optimal control. Systems and Control Letters, 21, pp 433-441 1993.

[94.1] Pierre Bernhard and Odile Pourtallier. Pursuit evasion game with costly information. Dynamics and Control 4 (Special issue in memory of John V. Breakwell.) pp 365-382.

[94.2] Pierre Bernhard. A Min-max certainty Equivalence Principle for Nonlinear Discrete Time Control problems. Systems and Control Letters 24, pp 229-234, 1994.

[94.3] Pierre Bernhard and Alain Rapaport. Min-max certainty equivalence principle and differential games. Sixth International Symposium on Differential Games and Applications, St Jovite, Canada, July 13-15 1994.

[94.4] Pierre Bernhard. Minimax versus stochastic partial information control. 33rd IEEE Conference on Decision and Control, Orlando, Fla, USA. 1994.

[95.1] Stéphane le Menec and Pierre Bernhard. Decision Support System for Medium Range Aerial Duels Combining Elements of Pursuit-Evasion Game Solutions with {AI} Techniques, Annals of the ISDG 3, pp 207-225, 1995.

[95.2] Pierre Bernhard. Expected Values, Feared Values and Partial Information Optimal Control. Annals of the ISDG 3, pp 3-24, 1995.

[95.3] Pierre Bernhard and Alain Rapaport. On a Theorem of Danskin with an Application to a Theorem of von {N}eumann-{S}ion}, Nonlinear Analysis, Theory, Methods and Applications, 24, pp 1163-1181, 1995.

[95.4] Alain Rapaport and Pierre Bernhard. Étude d'un jeu de poursuite plane avec connaissance imparfaite d'une coordonnée, APII, 29, pp 575-601, 1995

[95.5] Tamer Başar and Pierre Bernhard. H-infinity Optimal Control and Related Minimax Design Problems. (2nd edition). Birkhauser, (423 p.), 1995.

[96.1] Pierre Bernhard and Alain Rapaport. Min-max certainty equivalence principle and differential games. International Journal of Robust and Nonlinear Control, 6, pp 825-842, 1996.

[96.2] Pierre Bernhard. A separation theorem for expected value and feared value discrete time control. COCV, 1, pp 169-184, 1996.

[97.1] Georges Reversat, Jean-Pierre Rossi et Pierre Bernhard. Analyse des courbes de survie des némathodes par la méthode de Teissier. Compte rendu à l'Académie des Sciences, Sciences de la vie, 320, pp 259-266, 1997

[99.1] Pierre Bernhard and Naïra Hovakimyan. Nonlinear robust control and minimax team problems. International Journal of Robust and Nonlinear Control, 9, pp 239--257, 1999.

[00.1] Pierre Bernhard. Max-plus algebra and mathematical fear in dynamic optimization. Set Valued Analysis, 8, pp 71-84, 2000.

[01.1] Pierre Bernhard and Naïra Hovakimyan. Certainty equivalence principle and minimax team problems. Annals of the International Society of Dynamic Games 6:31-44, 2001. Also: 8th International Symposium of Dynamc games and Applications, Maastricht, The Netherlands, 1998.

[01.2] Pierre Bernhard, Stéphane Crepey and Alain rapaport.Comparison of two numerical schemes for barrier and value of a simple pursuit-evasion game. Annals of the International Society of Dynamic Games 6, pp 253-273, 2001. Also: 8th International Symposium of Dynamc games and Applications, Maastricht, The Netherlands, 1998.

[02.1] Pierre Bernhard, Naima El Farouq and Stéphane Thiery. An impulsive differential game arising in finance with interesting discontinuities. 10th ISDG International Symposium on Dynamic Games and Applications, Saint Petersburg, 2002, also Annals of the International Society of Dynamic Games 8, pp 335-363, 2006.

[02.2] Pierre Bernhard. A survey of linear quadratic robust control. Macroeconomics Dynamics 6, pp 19-39, 2002.

[03.1] Pierre Bernhard. Minimax —or Ferad Value– L1/L-infinity Control. Theoretical Computer Science, 293, pp 25-44, 2003.

[03.2] Pierre Bernhard. A robust control approach to option pricing. In Mark Salmon, editor: Applications of Robust Decision Theory and Ambiguity in Finance, City University Press, 2003.

[05.1] Pierre Bernhard. A robust control approach to option pricing including transaction costs. Annals of the ISDG, 7, pp 391–416, 2005.

[05.2] Arik Melikyan and Pierre Bernhard. Geometry of optimal trajectories around a focal singular surface in differential games. Applied Mathematics and Optimization, 52, pp 23–37, 2005.

[05.3] Pierre Bernhard. Chain differentials with an application to the mathematical fear operator. Nonlinear Analysis, 62, pp 1225–1233, 2005.

[05.4] Pierre Bernhard. The robust control approach to option pricing and interval models: an overview. In Michèle Breton and Hatem Ben-Ameur, editors, Numerical Methods in Finance, pages 91–108. Springer, New York, 2005.

[05.5] Pierre Bernhard. On the singularities of an impulsive differential game arising in mathematical finance. International Game Theory Review, 8, pp 219-229, 2005.

[05.6] Éric Wajnberg, Pierre Bernhard, Frédéric Hamelin, and Guy Boivin. Optimal patch time allocation for time limited foragers. Behavioural Ecology and Sociobiology, 60, pp 1–10, 2005.

[05.7] Pierre Bernhard and Anikal J. Shaiju. Evolutionary stable strategies and dynamics: Tutorial, example and open problems. In Guiomar Martin-Herran and Georges Zaccour, editors, 5th ISDG Workshop, Segovia, Spain, September 21–24, 2005.

[06.1] A.J. Shaiju and Pierre Bernhard. Evolutionarily stable strategies: Two nontrivial examples and a theorem. In 12th International Symposium on Dynamic Games and Applications, Sophia Antipolis, France, 2006. Also in P. Bernhard, V. Gaitsgory and O. Pourtallier ed.: Advances in Dynamic Games and their Applications, Annals of the ISDG 10, pp 377-398, Birkhauser, 2009.

[06.2] Stéphane Thiery, Pierre Bernhard, and Geert-Jan Olsder. Robust Control Approach to Digital Option Pricing: Synthesis Approach. 12th International Symposium on Dynamic Games and Applications, Sophia Antipolis, France, 2006. Also in P. Bernhard, V. Gaitsgory and O. Pourtallier ed.: Advances in Dynamic Games and their Applications, Annals of the ISDG 10, pp 293-310, Birkhauser, 2009.

[07.1] Eitan Altman, Pierre Bernhard, Merouane Debbah, and Alonso Silva. Contiunum equilibria for routing in dense ad-hoc networks. In Allerton Conference on Communication, Control, and Computing, number 45, Allerton House, Monticello, Il., USA, 2007. See also Computer Networks 54, pp 1005-1018, 2010.

[07.2] Pierre Bernhard, Naïma El Farouq, and Stéphane Thiery. Robust control approach to option pricing: representation theorem and fast algorithm. SIAM Journal on Control and Optimization, 46, pp 2280–2302, 2007.

[07.3] Frédéric Hamelin, Pierre Bernhard, A.J. Shaiju, and Eric Wajnberg. Diet selection as a differential foraging game. SIAM journal on Control and Optimization, 46, pp 1539–1561, 2007.

[07.4] Frédéric Hamelin, Pierre Bernhard, and Éric Wajnberg. Superparasitism as a differential game. Theoretical Population Biology, 72, pp 366–378, 2007.

[07.5] Bernard Roitberg and Pierre Bernhard. State dependent problems for parasitoids: case studies and solutions. In Eric Wajnberg, Carlos Bernstein, and Jacques van Alphen, editors, Behavioural Ecology of Insect Parasitoids. Blackwell, pp 337-356. 2007.

[07.8] Frédéric Hamelin, Pierre Bernhard, Philippe Nain, and Éric Wajnberg. Foraging under competition: evolutionarily stable patch-leaving strategies with random arrival times. 1. scramble competition. In Thomas Vincent, editor, Advances in Dynamic Game Theory, volume 9 of Annals of the ISDG, pp 327–348. 2007.

[07.9] Frédéric Hamelin, Pierre Bernhard, A.J. Shaiju, and Éric Wajnberg. Foraging under competition: evolutionarily stable patch-leaving strategies with random arrival times. 2 interference competition. In Thomas Vincent, editor, Advances in Dynamic Game Theory, volume 9 of Annals of the ISDG, pp 349–365. 2007.

[08.1] Andrei Akhmetzhanov, Pierre Bernhard, Frédéric Grognard, and Ludovic Mailleret. Reproduction dynamics in a differential game between foraging predators and hiding preys. In International Symposium on the theory and applications of dynamic games, number 13, Wroclaw, Poland, 2008.

[08.2] Pierre Bernhard. Ess, population games, replicator dynamics: dynamics and games if not dynamic games. In International Symposium on the theory and applications of dynamic games, number 13, 2008. Also in Krzysztof Szajowski and Georges Zaccour ed. Advances in the Theory and Applications of Dynamic Games, Annals of the ISDG 11, Birkhaüser, 2010.

[08.3] Pierre Bernhard and Frédéric Hamelin. Two-by-two static, evolutionary, and dynamic games. In Yves Bertot, Gérard Huet, Jean-Jacques Lévy and Gordon Plotkin, editors, From Semantics to Computer Science: Essays in Honor of Gilles Kahn, pp 452–474. Cambridge University Press, 2008.

[08.4] Frédéric Hamelin and Pierre Bernhard. Uncoupling Isaacs equations in two-player nonzero-sum differential games. Conflict over parental care as an example. Automatica, 44, pp 882–885, 2008.

[08.5] Eitan Altman, Pierre Bernhard, and Alonso Silva. The Mathematics of Routing in Massively Dense Ad-Hoc Networks, International Conference on Ad-Hoc Networks and Wireless, Sophia Antipolis, France, 2008.

[08.6] Alonso Silva, Pierre Bernhard, and Eitan Altman. Numerical solutions of continuum equilibria for routing in dense ad-hoc networks. Interperf: Workshop on Interdisciplinary Systems Approach in Performance Evaluation and Design of Computer Communication Systems. Athens, Greece, 2008.

[09.1] Pierre Bernhard, Vladimir Gaitsgory, and Odile Pourtallier. Advances in Dynamic Games and their Applications: Analytical and Numerical Developments, volume 10. Sringer/Birkhäuser, Boston, 2009.

[09.2] Andrei Akhmetzhanov, Pierre Bernhard, Frédéric Grognard, and Ludovic Mailleret. Competition between foraging predators and a hiding preys as a nonzero-sum differential game. In Gamenets 2009, Istanbul, Turkey, 2009.

[09.3] Pierre Bernhard. Nonzero-sum dynamic games in the managment of biological systems. Third International Conference on Game Theory and Managment, Sankt Petersburg, Russia, 2009.

[10.1] Naïma El Farouq, Guy Barles, and Pierre Bernhard. Deterministic minimax impulse control. Applied Mathematics and Optimization 61, pp 353-378, 2010.

[10.2] Pierre Bernhard and Naïma El Farouq A Robust Control Approach to Option Pricing: the Uniqueness Theorem. EPSRC Symposium Workshop on game theory for finance, social and biological sciences, University of Warwick, U.K., 2010. (Also in in L. Petrosjan and V. Mazalov eds. Game Theory and Applications 16, Nova Science Publishers, pp 1-18. 2013)

[10.3] Pierre Bernhard, Frédéric Grognard, Ludovic Mailleret, and Andrei Akhmetzhanov. ESS for life history of cooperating consumers facing cheating mutants. 14th International Symposium on Dynamic Games and Applications, Banff, Canada, 2010.

[10.4] Andrei Akhmetzhanov, Frédéric Grognard, Ludovic Mailleret, and Pierre Bernhard. Join forces or cheat: evolutionary analysis of a consumer-resource system. 14th International Symposium on Dynamic Games and Applications, Banff, Canada, 2010.

[10.5] Eitan Altman, Pierre Bernhard, Stéphane Caron, Georges Kesidis, Julio Rojas-Mora, and Sulan Wong. A Study of Non-Neutral Networks with Usage-based Prices. 3rd ETM Workshop, Amsterdam, The Netherlands, 2010, also in Telecommunications and Regulated Industries eJournal, 2010.

[11.1] Andrei Akhmetzhanov, Pierre Bernhard, Frédéric Grognard, and Ludovic Mailleret. Dynamic game for optimal resource allocation of annual plants and grazing consumer. European Conference on Mathematical and Theoretical Biology, 2011.

[12.1] Pierre Bernhard et al. The Interval Market Model in Mathematical Finance: a Game Theoretic Approach. (357 p.) Birkhaüser. 2012.

[14.1] Pierre Bernhard and Frédéric Hamelin. Simple signaling games of sexual selection (Grafen's revisited). Journal of Mathematical Biology 69, pp. 1719-1742.

[14.2] Pierre Bernhard, Linear quadratic zero-sum two-person differential games, in J. Bailleul and T. Samad ed.: Encyclopaedia of Systems and Control, Springer, pp 649-653, 2014.

[14.3] Pierre Bernhard, Pursuit-evasion games and zero-sum two-person differential games, in J. Bailleul and T. Samad ed.: Encyclopaedia of Systems and Control, Springer, pp 1103-1109, 2014.

[15.1] Naïma el farouq and Pierre Bernhard. Proportional transaction costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem. Applied Mathematics and Optimization 72, pp 187-202 2015.

[15.2] Pierre Bernhard. Evolutionary Dynamics of the Handicap Principle: An Example. Dynamic Games and Applications 5, pp 214-227. 2015.

[16.1] Pierre Bernhard and Frédédic Hamelin. Sharing a resource with randomly arriving foragers. Mathematical Biosciences 273, pp 91--101, 2016.

[17.1] Pierre Bernhard and Marc Deschamps. On dynamic games with randomly arriving players, Dynamic Games and Applications, 7, pp 360-385, 2017

[18.1] Pierre Bernhard. Robust Control and Dynamic Games. (30 p., 2016) In T. Basar and G. Zaccour editors: Handbook of Dynamic Games, Springer. 2018.

Rapports et conférences non (encore) publiés

[74.3] Pierre Bernhard. Reduced size optimal control laws. Technical meeting of the AGARD avionics panel, Athens, Greece, 1974.

[89.3] Pierre Bernhard. Boundary value problems and dynamical games.

[91.6] Pierre Bernhard. A lecture on the game theoretic approach to H-infinity control. France-Italy-USSR Symposium on Numerical Mathematics and Applications. Sophia Antipolis, France. 1991.

[92.5] Pierre Bernhard et Robert Fournier. Parallélisation de la recherche d'une trajectoire d'approche d'astéroïdes. Rapport technique INRIA, 1992.

[92.6] Pierre Bernhard. Differential games: a lecture on the Isaacs-Breakwell theory. Summer School on Differential Games, (Gianni Ricci ed.) Italian Network on Game Theory, Cagliari, Italy, 1992.

[93.3] Pierre Bernhard. Sketch of a theory of nonlinear partial information min-max control. IRIA technical report # 2020, 1993.

[98.1] Pierre Bernhard. Isaacs, Breakwell, and their sons. 8th ISDG International Symposium on the Theory an Applications of Differential Games, Maastricht, The Netherlands. 1998.

[07.6] Éric Wajnberg, Frédéric Hamelin, Pierre Bernhard, and Guy Boivin. Durée optimale de l’exploitation des agrégats d’hôtes par des insectes parasitoïdes à durée de vie limitée : approche théorique et vérification expérimentale. In 134 ème réunion de la Société d’Entomologie du Québec, Montréal, Canada. 2007.

[07.7] Pierre Bernhard, Stéphane Thiery, and Marc Deschamps. La tarification d’options : proposition pour une approche déterministe. In Congrès annuel de l’Association Française des Sciences Economiques, 56, Paris, 2007.

[11.2] Pierre Bernhard. Robust Optimization in Finance. Optimization Days, GERAD, HEC, Montréal, Canada. 2011.

[13.1] Pierre Bernhard and Frédéric Hamelin. Games of sexual selection: static and dynamic aspects. International Workshop on Biodiversity and Environment: Viability and Dynamic Games Perspective. Centre de Recherches Mathématiques, Université de Montréal. 2013.

[14.4] Pierre Bernhard. Modeling and control in physical, life, and social sciences: Some remarks. At the Boundaries of Dynamic Games, Control, and Viability. St Nicolas-la-Chapelle, France. 2014.

[16.3] Pierre Bernhard and Marc Deschamps. Dynamic equilibrium in games with randomly arriving players. (Bio-engineering version) INRIA Research report RR-8961, 2016.(See also economic science version as working paper CRESE, Université de Bourgogne-Franche Comté)

[16.4] Pierre Bernhard and Marc Deschamps. Cournot oligopoly with randomly arriving producers. Working paper, CRESE, Université de Bourgogne-Franche Comté, 2016.

[17.2] Pierre Bernhard and Marc Deschamps. Kalman, beyond the filter. 2017.

Notes éparses

[03.3] Pierre Bernhard. Kolmogorov, Kuhn, Isaacs et Bellman. 2003

[05.8] Pierre Bernhard. Théorie spectrale des matrices max + et leurs puissances successives. 2005

[12.1] Pierre Bernhard. Des planimètres. 2012

[13.1] Pierre Bernhard. Quantitative natural selection. 2013

[15.3] Pierre Bernhard (with Eric Wajnberg). LMC and MVT match together, 2015.

[15.4] Pierre Bernhard. Le Principe des petits nombres, ou premier théorème de Lapalice. (Suivi des deuxième et troisième théorèmes du même logicien.) 2015

[15.5] Pierre Bernhard. Critical comments of ``Mathematical Understanding of Nature'' by V. I. Arnold (2014), 2015.

[17.1] Pierre Bernhard. Discrete time Carathéodory's canonical equations. 2017

Notes de cours

[LQ] Formulaire Linéaire quadratique (LQG et H-infini)

[EDO] Équations différentielles ordinaires

[Opt ing] Éléments d'optimisation (Ecole Polytech'Nice)

[Opt math] Éléments d'optimisation (Maîtrise de mathématiques appliquées)

[Portefeuille] Optimisation de portefeuille