Director of Research (if dissertation) or Advisor (if thesis)
Raginsky, Maxim
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Markov Chain
Information Theory
Control
Limited capacity
Optimization
Abstract
This thesis poses a general model for optimal control subject to information
constraint, motivated in part by recent work on information-constrained
decision-making by economic agents.
In the average-cost optimal control framework, the general model introduced
in this paper reduces to a variant of the linear-programming representation
of the average-cost optimal control problem, subject to an additional
mutual information constraint on the randomized stationary policy. The resulting
in nite-dimensional convex program admits a decomposition based
on the Bellman error, which is the subject of study in approximate dynamic
programming.
Later, we apply the general theory to an information-constrained variant
of the scalar Linear-Quadratic-Gaussian (LQG) control problem. We give
an upper bound on the optimal steady-state value of the quadratic performance
objective and present explicit constructions of controllers that achieve
this bound. We show that the obvious certainty-equivalent control policy is
suboptimal when the information constraints are very severe, and propose
another policy that performs better in this low-information regime. In the
two extreme cases of no information (open-loop) and perfect information,
these two policies coincide with the optimum.
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