Uncertainty, dualism and inverse reachable sets

A specification in the language of the theory of categories is given for dynamic models with uncertainty. For continuous models the uncertainty is treated by means of differential inclusions. The reversibility and the inverse problem are considered. It is shown that models with uncertainty are not reversible (cannot be solved simply reversing the time). The inverse problem for such models is solved using the concept of dualism in the theory of categories. The categorical language is much more abstract and the categorical specification may work in continuous case as well in the discrete event simulation.