A Basic Theory for Available Operation of Extremely Complicated Large-Scale Network Systems

Kazuo HORIUCHI

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A    No.10    pp.2232-2238
Publication Date: 2007/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.10.2232
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Systems Theory and Control
Keyword: 
extremely complicated large-scale network system,  available operation,  fixed point theorem,  system of set-valued operator equations,  ball measure of non-compactness,  

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Summary: 
In this paper, we shall describe about a basic theory based on the concept of set-valued operators, suitable for available operation of extremely complicated large-scale network systems. Fundamental conditions for availability of system behaviors of such network systems are clarified in a form of fixed point theorem for system of set-valued operators. Here, the proof of this theorem is accomplished by the concept of Hausdorff's ball measure of non-compactness.

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