Aos
Algebra of Systems: An Executable Framework for Model Synthesis and
Evaluation
Benjamin H.-Y. Koo
Tsinghua University
Department of Industrial Engineering
Beijing 100084 P. R. China
benkoo@tsinghua.edu.cn
Willard L. Simmons, Edward F. Crawley
Massachusetts Institute of Technology
Department of Aeronautics and Astronautics
77 Mass. Ave., Cambridge, MA 02130, USA
wsimmons@mit.edu, crawley@mit.edu
Abstract
This paper represents system models as algebraic entities
and formulates the model transformation activities as
algebraic operations. We call this modeling framework “Algebra
of Systems” (AoS). To show that AoS can automate
complex model reasoning tasks in system design projects,
we implemented the abstract algebraic specification as an
executable meta-language named Object-Process Network
(OPN), which serves as a tool for automatic model transformation,
enumeration and evaluation. A case study of the
Apollo lunar landing mission design is developed using this
algebraic modeling approach.
1 Introduction
When reasoning about complex systems, it is often necessary
to decompose the system into smaller units of abstraction,
and then represent interactions among the units.
The objective of this paper is to present a mathematical
framework called Algebra of Systems (AoS), which provides
an formal structure to reason about system of elements
and interactions in terms of algebraic operands and
operators. To automate the algebraic manipulation of system
models, we also implement an executable modeling
language, Object-Process Network (OPN) that follows the
formalisms defined in AoS.
An algebra is a mathematical structure made up of
two kinds of things: an operand set, and an operator set.
The operators for...
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