Modeling of symbolic systems

Part II - Hilbert space construction for model identification and order reduction

Yicheng Wen, Asok Ray, Ishanu Chattopadhyay, Shashi Phoha

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

3 Citations (Scopus)

Abstract

This paper, which is the second of two parts, is built upon the vector space of symbolic systems represented by probabilistic finite State automata (PFSA) reported in the first part. This second part addresses the Hilbert space construction for model identification, where order reduction is achieved via orthogonal projection. To this end, a family of inner products is constructed and the norm induced by an inner product is interpreted as a measure of information contained in the PFSA, which also quantifies the error due to model order reduction. A numerical example elucidates the process of model order reduction by orthogonal projection from the space of PFSA onto a subspace that belongs to the class of shifts of finite type.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 American Control Conference, ACC 2011
Pages5139-5144
Number of pages6
StatePublished - Sep 29 2011
Event2011 American Control Conference, ACC 2011 - San Francisco, CA, United States
Duration: Jun 29 2011Jul 1 2011

Other

Other2011 American Control Conference, ACC 2011
CountryUnited States
CitySan Francisco, CA
Period6/29/117/1/11

Fingerprint

Hilbert spaces
Finite automata
Identification (control systems)
Vector spaces

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Wen, Y., Ray, A., Chattopadhyay, I., & Phoha, S. (2011). Modeling of symbolic systems: Part II - Hilbert space construction for model identification and order reduction. In Proceedings of the 2011 American Control Conference, ACC 2011 (pp. 5139-5144). [5990620]
Wen, Yicheng ; Ray, Asok ; Chattopadhyay, Ishanu ; Phoha, Shashi. / Modeling of symbolic systems : Part II - Hilbert space construction for model identification and order reduction. Proceedings of the 2011 American Control Conference, ACC 2011. 2011. pp. 5139-5144
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Wen, Y, Ray, A, Chattopadhyay, I & Phoha, S 2011, Modeling of symbolic systems: Part II - Hilbert space construction for model identification and order reduction. in Proceedings of the 2011 American Control Conference, ACC 2011., 5990620, pp. 5139-5144, 2011 American Control Conference, ACC 2011, San Francisco, CA, United States, 6/29/11.

Modeling of symbolic systems : Part II - Hilbert space construction for model identification and order reduction. / Wen, Yicheng; Ray, Asok; Chattopadhyay, Ishanu; Phoha, Shashi.

Proceedings of the 2011 American Control Conference, ACC 2011. 2011. p. 5139-5144 5990620.

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

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Wen Y, Ray A, Chattopadhyay I, Phoha S. Modeling of symbolic systems: Part II - Hilbert space construction for model identification and order reduction. In Proceedings of the 2011 American Control Conference, ACC 2011. 2011. p. 5139-5144. 5990620