Séance TB10 - Contrôle stochastique / Stochastic Control
Jour mardi, le 8 mai 2007 Salle Demers Beaulne Président Roland Malhamé
Présentations
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13h30- 13h55 |
The Nash Certainty Equivalence and McKean Vlasow Systems |
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Huang Minyi, Australian National University, RSISE, Ian Ross Building 31, Canberra, ACT, Australia, 0200 Caines Peter, McGill University, Electrical Engineering, 3480 rue Université, Montréal, Québec, Canada, H3A 2A7 Malhamé P. Roland, GERAD et École Polytechnique de Montréal, Génie Électrique, C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7 In the large stochastic ensembles of statistical mechanics, the McKean Vlasow equations express a consistency relation, if it exists, between the time varying probability distribution function associated with a given random particle and the empirical distribution of neighboring particles interacting with it. We developed a controlled version of the McKean Vlasow equation in the context of large scale stochastic dynamic games. |
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13h55- 14h20 |
Nash Equilibrium Based Synthesis of Collective Motion |
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Huang Minyi, Australian National University, RSISE, Ian Ross Building 31, Canberra, ACT, Australia, 0200 Malhamé P. Roland, GERAD et École Polytechnique de Montréal, Génie Électrique, C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7 Caines Peter, McGill University, Electrical Engineering, 3480 rue Université, Montréal, Québec, Canada, H3A 2A7 The problem of controlling the motion of large ensembles of moving individual agents such as swarms, fish schools or large collections of micro robots in space exploration, in a decentralized manner is considered. Individuals follow random exploratory trajectories but must be careful not to drift too much away from the group. Optimal trajectories are sought within the framework of large scale stochastic games. |
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14h20- 14h45 |
The Nash Certainty Equivalence Principle for Networks Driven by Point Processes |
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Zhongzing Ma, Mc Gill University, Electrical and Computer Engineering Department, 3480 University Street, Montreal, Quebec, Canada, H3A 2A7 Caines Peter, McGill University, Electrical Engineering, 3480 rue Université, Montréal, Québec, Canada, H3A 2A7 Malhamé P. Roland, GERAD et École Polytechnique de Montréal, Génie Électrique, C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7 We consider optimal admission and routing control problems in so-called loss network systems (rejected call requests are lost). The Hamilton-Jacobi-Bellman equations of the optimal stochastic control problem are derived. When all processes are Poisson, they correspond to Markov decision problems of immense dimension. A more tractable, but suboptimal, large scale stochastic dynamic games framework is then considered. |
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14h45- 15h10 |
Martingale Methods for the Development of Mean Field Equations |
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David R. McDonald, University of Ottawa, Department of Mathematics and Statistics, 585 King Edward, Ottawa, Ontario, Canada, K1N 615 A brief tutorial is presented on martingale methods for the development of mean field equations for Markov processes, in particular as expounded by Carl Graham. Applications are reported. |