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2003-09-30Buch DOI: 10.18452/8300
Dual effect free stochastic controls
dc.contributor.authorBarty, Kengy
dc.contributor.authorCarpentier, P.
dc.contributor.authorChancelier, J.-P.
dc.contributor.authorCohen, G.
dc.contributor.authorLara, M. de
dc.contributor.authorGuilbaud, T.
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T19:54:00Z
dc.date.available2017-06-16T19:54:00Z
dc.date.created2006-03-01
dc.date.issued2003-09-30
dc.date.submitted2003-03-03
dc.identifier.urihttp://edoc.hu-berlin.de/18452/8952
dc.description.abstractIn 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.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematik
dc.titleDual effect free stochastic controls
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10059151
dc.identifier.urnurn:nbn:de:kobv:11-10059169
dc.identifier.doihttp://dx.doi.org/10.18452/8300
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.pages26
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2003
local.edoc.container-issue18
local.edoc.container-erstkatid2936317-2

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