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Optimal Decisions with Limited Information

Gattami, Ather LU (2007) In PhD Theses TFRT-1079.
Abstract (Swedish)
Popular Abstract in Swedish

Denna avhandling behandlar statiska och dynamiska lagbeslutsproblem i både stokastiska och deterministiska ramverk. Lagproblemet är ett kooperativt spel, där ett antal spelare utgör ett lag som försöker optimera en given kostnad inducerad av omvärldens osäkerhet. Osäkerheten kan modelleras antingen som stokastisk, vilket ger upphov till det stokastiska lag problemet, eller som deterministisk där laget försöker optimera värsta fallet scenariot. Båda de stokastiska och deterministiska statiska lagproblemen är uppställda och lösta i det linjär-kvadratiska ramverket. Det dynamiska lag problemet är formulerat genom välkända resultat från grafteorin. Den dynamiska kopplingens struktur beskrivs av en... (More)
Popular Abstract in Swedish

Denna avhandling behandlar statiska och dynamiska lagbeslutsproblem i både stokastiska och deterministiska ramverk. Lagproblemet är ett kooperativt spel, där ett antal spelare utgör ett lag som försöker optimera en given kostnad inducerad av omvärldens osäkerhet. Osäkerheten kan modelleras antingen som stokastisk, vilket ger upphov till det stokastiska lag problemet, eller som deterministisk där laget försöker optimera värsta fallet scenariot. Båda de stokastiska och deterministiska statiska lagproblemen är uppställda och lösta i det linjär-kvadratiska ramverket. Det dynamiska lag problemet är formulerat genom välkända resultat från grafteorin. Den dynamiska kopplingens struktur beskrivs av en graf. Det visar sig vara naturligt att använda en grafteoretisk formulering för att undersöka hur ett beslut av en lagmedlem påverkar de andra i laget. Villkor för lösbarheten av det dynamiska lagproblemet ges i termer av grafstrukturen. Dessa villkor visar nya strukturer som ger lösbara problem, vilket utvidgar befintliga resultat. För denna nya klass av strukturer, ges nödvändiga och tillräckliga villkor för stabiliserbarhet av de sammankopplade systemen. Tillståndsåterkoppling för de stokastiska och deterministiska dynamiska lagproblemen löses genom ett nytt angreppssätt. Detta nya angreppsätt är baserat på den kritiska ideen om störningsåterkoppling, vilket används för att separera styrningseffekten från utsignalen, för att eliminera styrningens duala roll. Slutligen behandlas ett generaliserat stokastiskt linjär-kvadratiskt reglerproblem. En bred klass av lagproblem kan modelleras genom att införa kvadratiska begränsningar av korrelations typ. Begränsningar på styrsignaler är väldigt vanliga, och även dessa kan modelleras med hjälp av kvadratiska bivillkor. Detta motiverar utvecklkingen av en generaliserad reglerteori med kvadratiska bivillkor för både den ändliga och oändliga tidshorisonten. Lösningen kan hittas genom ändligtdimensionell konvex optimering. (Less)
Abstract
This thesis considers static and dynamic team decision problems in both stochastic and deterministic settings. The team problem is a cooperative game, where a number of players make up a team that tries to optimize a given cost induced by the uncertainty of nature. The uncertainty is modeled as either stochastic, which gives the stochastic team problem, or modelled as deterministic where the team tries to optimize the worst case scenario. Both the stochastic and deterministic static team problems are stated and solved in a linear quadratic setting. It is shown that linear decisions are optimal in both the stochastic and deterministic framework. The dynamic team problem is formulated using well known results from graph theory. The dynamic... (More)
This thesis considers static and dynamic team decision problems in both stochastic and deterministic settings. The team problem is a cooperative game, where a number of players make up a team that tries to optimize a given cost induced by the uncertainty of nature. The uncertainty is modeled as either stochastic, which gives the stochastic team problem, or modelled as deterministic where the team tries to optimize the worst case scenario. Both the stochastic and deterministic static team problems are stated and solved in a linear quadratic setting. It is shown that linear decisions are optimal in both the stochastic and deterministic framework. The dynamic team problem is formulated using well known results from graph theory. The dynamic interconnection structure is described by a graph. It appears natural to use a graph theoretical formulation to examine how a decision by a member of the team affects the rest of the members. Conditions for tractability of the dynamic team problem are given in terms of the graph structure. Tractability of a new class of information constrained team problems is shown, which extends existing results. For the presented tractable classes, necessary and sufficient conditions for stabilizability are given.



The state feedback $mathcal{H}_2$ and $mathcal{H}_{infty}$ dynamic team problems are solved using a novel approach. The new approach is based on the crucial idea of disturbance feedback, which is used to separate the controller effect from the measured output, to eliminate the controller's dual role. Finally, a generalized stochastic linear quadratic control problem is considered. A broad class of team problems can be modeled by imposing quadratic constraints of correlation type. Also, power constraints on the control signals are very common. This motivates the development of a generalized control theory for both the finite and infinite horizon case, where power constraints are imposed. It is shown that the solution can be found using finite dimensional convex optimization. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Dullerud, Geir, University of Illinois at Urbana-Champaign, USA
organization
publishing date
type
Thesis
publication status
published
subject
keywords
systems, numerical analysis, Computer science, Convex Optimization, Graph Theory, Team Decision Theory, Game Theory, control, Datalogi, numerisk analys, system, kontroll, Automation, robotics, control engineering, Automatiska system, robotteknik, reglerteknik
in
PhD Theses
volume
TFRT-1079
pages
127 pages
publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
defense location
Room E:1406, E-building Ole Römers väg 1 Lund University Faculty of Engineering
defense date
2007-06-08 13:15
ISSN
0280-5316
language
English
LU publication?
yes
id
c3adac11-2983-4ca0-bde3-05dec4561718 (old id 26864)
date added to LUP
2007-06-05 13:42:57
date last changed
2016-09-19 08:44:58
@phdthesis{c3adac11-2983-4ca0-bde3-05dec4561718,
  abstract     = {This thesis considers static and dynamic team decision problems in both stochastic and deterministic settings. The team problem is a cooperative game, where a number of players make up a team that tries to optimize a given cost induced by the uncertainty of nature. The uncertainty is modeled as either stochastic, which gives the stochastic team problem, or modelled as deterministic where the team tries to optimize the worst case scenario. Both the stochastic and deterministic static team problems are stated and solved in a linear quadratic setting. It is shown that linear decisions are optimal in both the stochastic and deterministic framework. The dynamic team problem is formulated using well known results from graph theory. The dynamic interconnection structure is described by a graph. It appears natural to use a graph theoretical formulation to examine how a decision by a member of the team affects the rest of the members. Conditions for tractability of the dynamic team problem are given in terms of the graph structure. Tractability of a new class of information constrained team problems is shown, which extends existing results. For the presented tractable classes, necessary and sufficient conditions for stabilizability are given.<br/><br>
<br/><br>
The state feedback $mathcal{H}_2$ and $mathcal{H}_{infty}$ dynamic team problems are solved using a novel approach. The new approach is based on the crucial idea of disturbance feedback, which is used to separate the controller effect from the measured output, to eliminate the controller's dual role. Finally, a generalized stochastic linear quadratic control problem is considered. A broad class of team problems can be modeled by imposing quadratic constraints of correlation type. Also, power constraints on the control signals are very common. This motivates the development of a generalized control theory for both the finite and infinite horizon case, where power constraints are imposed. It is shown that the solution can be found using finite dimensional convex optimization.},
  author       = {Gattami, Ather},
  issn         = {0280-5316},
  keyword      = {systems,numerical analysis,Computer science,Convex Optimization,Graph Theory,Team Decision Theory,Game Theory,control,Datalogi,numerisk analys,system,kontroll,Automation,robotics,control engineering,Automatiska system,robotteknik,reglerteknik},
  language     = {eng},
  pages        = {127},
  publisher    = {Department of Automatic Control, Lund Institute of Technology, Lund University},
  school       = {Lund University},
  series       = {PhD Theses},
  title        = {Optimal Decisions with Limited Information},
  volume       = {TFRT-1079},
  year         = {2007},
}