Determining a purely symbolic transfer function from symbol streams: Theory and algorithms

Christopher Griffin, Richard R. Brooks, Jason Schwier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Transfer function modeling is a standard technique in classical Linear Time Invariant and Statistical Process Control. The work of Box and Jenkins was seminal in developing methods for identifying parameters associated with classical (r, s, k) transfer functions. Discrete event systems are often used for modeling hybrid control structures and high-level decision problems. Examples include discrete time, discrete strategy repeated games. For these games, a discrete transfer function in the form of an accurate hidden Markov model of input-output relations could be used to derive optimal response strategies. In this paper, we develop an algorithm for creating probabilistic Mealy machines that act as transfer function models for discrete event dynamic systems (DEDS). Our models are defined by three parameters, (l1, l2, k) just as the Box-Jenkins transfer function models. Here l 1 is the maximal input history lengths to consider, l2 is the maximal output history lengths to consider and k is the response lag. Using related results, We show that our Mealy machine transfer functions are optimal in the sense that they maximize the mutual information between the current known state of the DEDS and the next observed input/output pair.

Original languageEnglish (US)
Title of host publication2008 American Control Conference, ACC
Pages4065-4067
Number of pages3
DOIs
StatePublished - Sep 30 2008
Event2008 American Control Conference, ACC - Seattle, WA, United States
Duration: Jun 11 2008Jun 13 2008

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2008 American Control Conference, ACC
CountryUnited States
CitySeattle, WA
Period6/11/086/13/08

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    Griffin, C., Brooks, R. R., & Schwier, J. (2008). Determining a purely symbolic transfer function from symbol streams: Theory and algorithms. In 2008 American Control Conference, ACC (pp. 4065-4067). [4587129] (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2008.4587129