Decomposition of Time Scales in Linear Systems and Markovian Decision Processes
Phillips, Randolph Gale
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/66245
Description
Title
Decomposition of Time Scales in Linear Systems and Markovian Decision Processes
Author(s)
Phillips, Randolph Gale
Issue Date
1981
Department of Study
Electrical Engineering
Discipline
Electrical 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
The presence of "slow" and "fast" dynamics in large scale systems has motivated the use of singular perturbations as a means of obtaining reduced order models for analysis and control law design. In this thesis we establish how systems having this "two-time-scale" property can use singular perturbation modeling to make this property explicit enabling various reduced order analysis and design techniques to be applied. For deterministic linear time-invariant systems, various techniques for obtaining reduced order models are unified through left and right eigenspace decompositions. A general two stage control design procedure for separate fast and slow subsystems is developed which can be applied to both continuous and discrete time models. Finally, Markov chain models of stochastic systems with "weak" and "strong" transition probabilities lead to a singularly perturbed model from which we obtain the concept of the reduced order "aggregate" chain. For controlled Markov chains the aggregate model is used to develop decentralized optimization algorithms for the discounted and average cost per stage problems.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
