Evaluation of Crisis, Reversibility, Alert Management for Constrained Dynamical Systems Using Impulse Dynamical Systems

Considering constrained dynamical systems characterized by a differential inclusion x′ ∈ F (x), we are interested in studying the situation where, for various reasons, the state leaves the constrain domain K either because the initial position does not belong to the Viability Kernel of K for F or it belongs to a “sustainable or tolerable” but not “comfortable” domain. This question appears in numerous models in Social Sciences or in Genetics as well as for controlling security in Automatics and Robotics, like Aircraft landing, rolling and taking off. After recalling basic concepts in Viability Theory and using hybrid calculus, we show how to evaluate and manage crisis in general cases.