Behavioral interpretation of the object-oriented paradigm for interconnected dynamic system modeling

Abstract

This article presents a mathematical interpretation of the object-oriented modeling paradigm inspired from the Willems' behavioral approach of systems theory. The object modeling of interconnected dynamic systems is introduced independently from any computer language and expressed as a set computation problem. Two behavioral representations (complete and partial) of an object are defined. Three object relationships, i.e. instantiation, composition and generalization are examined in the behavioral framework. Each definition is illustrated by basic examples, e.g. a storage tank, a resistor, a control valve and an electrical circuit. The implementation of the behavioral representations into the object-oriented language Modelica is finally presented.

Keywords:

• Object-modeling techniques
• Mathematical models
• Dynamic systems
• Complex systems

Notes

†In systems theory, the causality notion involves physical realizability. A system is noncausal if its response occurs prior to the input stimulus and causal otherwise. Herein, the question is which variable is caused by the other? If there is an invariant solution the system is causal but if there is no solution, e.g. the chicken-egg problem, the system is regarded as noncausal.