Fearful symmetry in system structures

Discusses the relationship between the level of symmetry in a system structure and loss of controllability. For a system consisting of a large number of modules, symmetrical structure is considered as the identity of modules and their interconnections. We especially deal with three basic structures: ring-type, bus-type and star-type structures. If the entire system becomes uncontrollable because of failures in a set of k submodules, this number k indicates the level of fault tolerance. On the other hand, the level of symmetry is evaluated by the number of transformations that keep the structure invariant. Through evaluation of the fault tolerance of the three basic structures, we consider the relationship between lowering the level of symmetry and the loss of controllability because of failures.

[1]  Arnold Kaufmann,et al.  Mathematical Models for the Study of the Reliability of Systems , 1977 .

[2]  W. Miller.  Symmetry groups and their applications , 1972 .

[3]  Hirokazu Ihara,et al.  Autonomous Decentralized Computer Control Systems , 1984, Computer.

[5]  Masaru Omura,et al.  Hi-Cell system architecture for manufacturing systems , 1995, Proceedings ISADS 95. Second International Symposium on Autonomous Decentralized Systems.

[6]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .

[7]  R. Tanaka,et al.  Structural analysis of fault-tolerance for homogeneous systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[8]  Thomas Kailath,et al.  Linear Systems , 1980 .

[9]  M. Mesarovic,et al.  Theory of Hierarchical, Multilevel, Systems , 1970 .

[10]  Hirokazu Ihara,et al.  Autonomous Controllability of Decentralized System Aiming at Fault-Tolerance , 1981 .

[11]  S. Ogawa,et al.  A fault-tolerant subway passenger information control system-an object oriented approach based on broadcast communication , 1995, Proceedings ISADS 95. Second International Symposium on Autonomous Decentralized Systems.

[12]  M. Golubitsky,et al.  Fearful Symmetry: Is God a Geometer? , 1992 .

[13]  N. Sebe,et al.  Controllability of autonomous decentralized systems , 1994, ETFA '94. 1994 IEEE Symposium on Emerging Technologies and Factory Automation. (SEIKEN) Symposium) -Novel Disciplines for the Next Century- Proceedings.