Abstract
The purpose of this note is to attract attention to what is called the elimination problem, which we believe to be an important but largely open problem in mathematical modelling. A typical way of modelling dynamical systems is by the method of hierarchical tearing and zooming: a system is decomposed into subsystems until a level is reached where the subcomponents have mathematical models that are assumed to be “known”. This procedure is described for example in [17]. Electrical circuits and robotic kinematic chains form the prototype examples of this sort of first principles modelling. These ideas also lie at the basis of modelling concepts as bond-graphs and object-oriented computer-assisted procedures used frequently for instance in chemical process modelling.
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Mareels, I., Willems, J.C. (1999). Elimination of latent variables in real differential algebraic systems. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_29
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