|edoc-Server der Humboldt-Universität zu Berlin|
Kengy Barty, CERMICS, École nationale des ponts et chaussées, Marne la Valleé|
P. Carpentier, ENSTA, Paris
J.-P. Chancelier, CERMICS, École nationale des ponts et chaussées, Marne la Valleé
G. Cohen, CERMICS, École nationale des ponts et chaussées, Marne la Valleé; INRIA, Rocquencourt
M. de Lara, CERMICS, École nationale des ponts et chaussées, Marne la Valleé
T. Guilbaud, CERMICS, École nationale des ponts et chaussées, Marne la Valleé
|Title:||Dual effect free stochastic controls|
|Date of Acceptance:||30.09.2003|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
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|In stochastic optimal control, a key issue is the fact that "solutions" are searched for in terms of "feedback" over available information and, as a consequence, a major potential difficulty is the fact that present control may affect future available information. This is known as the "dual effect" of control. Given a minimal framework (that is, an observation mapping from the product of a control set and of a random set towards an observation set), we define open-loop lack of dual effect as the property that the information provided by observations under open-loop control laws is fixed, whatever the open-loop control. Our main result consists in characterizing the maximal set of closed-loop control laws for which the information provided by observations closed with such a feedback remains also fixed. We then address the multi-agent case. To obtain a comparable result, we are led to generalize the precedence and memory-communication binary relations introduced by Ho and Chu for the LQG problem, and to assume that the precedence relation is compatible with the memory-communication relation. When the precedence relation induces an acyclic graph, we prove that, when open-loop lack of dual effect holds, the maximal set of closed-loop control laws for which the information provided by observations closed with such a feedback remains fixed is the set of feedbacks measurable with respect to this fixed information. We end by studying the dual effect for discrete time stochastic input-output systems with dynamic information structure, for which the same result holds.|
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