Random generation of monotonic functions for Monte Carlo solution of qualitative differential equations

We present improvements to the function representation and generation method used in the Monte Carlo analysis of incomplete ordinary differential equations. Our method widens the scope of the technique to cover cases in which no envelopes have been specified for the function under consideration, the...

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Bibliographic Details
Published in:Automatica (Oxford) 2005-05, Vol.41 (5), p.739-754
Main Authors: Say, A.C. Cem, Nircan, A. Kutsi
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Function representations
Mathematical analysis
Mathematics
Miscellaneous
Monotonic functions
Monte Carlo simulation
Ordinary differential equations
Sciences and techniques of general use
Semiquantitative reasoning
System dynamics
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Summary:We present improvements to the function representation and generation method used in the Monte Carlo analysis of incomplete ordinary differential equations. Our method widens the scope of the technique to cover cases in which no envelopes have been specified for the function under consideration, thereby extending the applicability of the Monte Carlo approach to the full repertoire of models developed for qualitative reasoning algorithms, and paving the ground for the integrated operation of these two highly complementary techniques. Our new representation does not entail unjustified implicit assumptions about the shape of the generated functions, and provides better coverage of the space of models defined by the input specifications. Our simulator (M OC ASS IM) also has the capability of imposing additional restrictions (e.g., convexity) on function shapes, which is particularly useful when the Monte Carlo technique is applied for solving system dynamics problems.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2004.10.022