Fault-Tolerance of Control Systems with Dihedral Group Symmetry

• TANAKA Reiko

  Faculty of Science and Technology, Keio University

• MUROTA Kazuo

  Research Institute for Mathematical Sciences, Kyoto University

Abstract

This paper deals with the fault-tolerance of systems that are symmetric with respect to the dihedral group D_m. The group D_m generally represents the geometric symmetry of a regular m-gon. We reveal the underlying mathematical mechanism of the loss of controllability for D_m-symmetric systems induced by failures and derive a necessary and sufficient condition to retain the controllability despite a failure. Moreover, we show the minimum number of functioning modules needed to retain the controllability despite the failures. It serves for a quantitative evaulation of fault-tolerance.

Journal

• Transactions of the Society of Instrument and Control Engineers

  Transactions of the Society of Instrument and Control Engineers 35 (6), 806-813, 1999

  The Society of Instrument and Control Engineers

Keywords

• fault-tolerance
• dihedral group
• controllability

Details

• CRID: 1390001204501023232
• NII Article ID: 130003791533
• NII Article ID: 10004576235
• NII Book ID: AN00072392
• DOI: 10.9746/sicetr1965.35.806
• ISSN: 18838189
• ISSN: 04534654
• NDL BIB ID: 4771277
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I4771277
• Web Site: https://www.jstage.jst.go.jp/article/sicetr1965/35/6/35_6_806/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed