### 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 language | English (US) |
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Title of host publication | Proceedings of the 2011 American Control Conference, ACC 2011 |

Pages | 5139-5144 |

Number of pages | 6 |

State | Published - Sep 29 2011 |

Event | 2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011 |

### Other

Other | 2011 American Control Conference, ACC 2011 |
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Country | United States |

City | San Francisco, CA |

Period | 6/29/11 → 7/1/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2011 American Control Conference, ACC 2011*(pp. 5139-5144). [5990620]

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Modeling of symbolic systems

T2 - Part II - Hilbert space construction for model identification and order reduction

AU - Wen, Yicheng

AU - Ray, Asok

AU - Chattopadhyay, Ishanu

AU - Phoha, Shashi

PY - 2011/9/29

Y1 - 2011/9/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053153239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053153239&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781457700804

SP - 5139

EP - 5144

BT - Proceedings of the 2011 American Control Conference, ACC 2011

ER -