Optimal Decisions with Limited Information

Research output: ThesisDoctoral Thesis (monograph)

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.

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.

Details

Authors
  • Ather Gattami
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Control Engineering

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
Original languageEnglish
QualificationDoctor
Awarding Institution
Supervisors/Assistant supervisor
Award date2007 Jun 8
Publisher
  • Department of Automatic Control, Lund Institute of Technology, Lund University
Publication statusPublished - 2007
Publication categoryResearch

Bibliographic note

Defence details Date: 2007-06-08 Time: 13:15 Place: Room E:1406, E-building Ole Römers väg 1 Lund University Faculty of Engineering External reviewer(s) Name: Dullerud, Geir Title: Professor Affiliation: University of Illinois at Urbana-Champaign, USA ---

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