Dynamic multi-person optimization with weakly coupled agents
Srikant, Rayadurgam
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Permalink
https://hdl.handle.net/2142/22658
Description
Title
Dynamic multi-person optimization with weakly coupled agents
Author(s)
Srikant, Rayadurgam
Issue Date
1991
Doctoral Committee Chair(s)
Basar, Tamer
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
In this thesis, we study multiple decision maker problems where the decision makers are coupled through a small parameter $\epsilon$. The class of systems considered exhibit the common feature that when the weak coupling is completely absent (i.e., when the coupling parameter $\epsilon$ = 0), the problem decomposes into a number of independent tractable problems or into a single tractable problem, but when the coupling is strong the problem may be difficult to solve. We are interested in the intermediate case when the coupling is neither absent nor strong. The central idea behind the construction of approximate solutions is to start with the zeroth order solution (obtained by setting $\epsilon$ = 0) and iteratively obtain successively better approximations to the optimal or equilibrium solution. Specifically, we have studied LQG teams featuring a nonclassical information pattern, nonlinear deterministic differential games, LQG nonzero-sum games and Markov decision problems. In the case of LQG teams, we showed the existence of finite-dimensional linear controllers (FDLCs) which approximate the optimal cost to O($\epsilon$). Then, by restricting ourselves to the class of FDLCs, we obtained higher order approximations to the optimal cost by solving a sequence of single decision maker LQG stochastic control problems. In LQG nonzero-sum games, we established the existence of a finite-dimensional Nash equilibrium for small values of the coupling parameter; further, we also showed that this equilibrium solution is well-posed and admissible as $\epsilon$ tends to zero. For the class of nonlinear, nonzero-sum differential games, we considered two types of information structures. In the case of the open-loop information structure, we have shown that approximate Nash equilibria can be obtained by solving the zeroth order problems and a sequence of LQ optimal control problems. When the information structure is dynamic, the decomposition involves the solution of the zeroth order problems and a sequence of cost evaluations (no control involved) followed by static optimization problems. We have also shown the existence of solutions to Markov decision problems featuring nonclassical information under the assumption of a finite-control set. Through the weak-coupling approach, we have thus been able to identify a class of tractable problems which were long thought to be intractable.
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