On the Theory of Trajectory Tubes — A Mathematical Formalism for Uncertain Dynamics, Viability and Control

This paper is a survey on the theory of trajectory tubes for differential inclusions, which appears to be a relevant tool for modeling uncertain dynamics. It is motivated by results in nonlinear analysis, particularly, in viability theory for differential inclusions, as well as by recent achievements in the theory of estimation and control for systems with unknown but bounded uncertainties. The motivations for these studies come from applied areas and the rapidly increasing number of applications range from computer sciences and engineering to economics as well as ecological and biomedical modeling. The theory is constructive and has led to the development of effective tools of computational and graphic animation.