The overall objective of the group is to design, with from a system point of view, control laws, observers, fusion and monitoring algorithms for dynamical systems subject to failure in order to guarantee specified performances. We consider nonlinear continuous systems (represented by differential equations), discrete-event systems (represented by finite state automata or Petri Nets), and hybrid dynamical systems (specifically switching systems). The algorithms are designed to control and supervise the system in normal operation but also in situations where some components are faulty and disturb the system’s performance and missions. Our goal is thus to guarantee a specified level of dependability (availability, reliability, security, maintainability) by setting up a supervision system, which includes monitoring, estimation, data fusion and automatic control algorithms, allowing a better toleration of these failures. To design a system of supervision, it is necessary to have an accurate model of the system. One innovation of the group is to develop such models (graphical, structural, behavioral, functional, formal), including the faulty components and their effects, considering the multi-physical and energetic characteristics as in Bond Graph models, with different levels of abstraction and complexity adapted to the considered supervision objectives. We consider all stages of the supervision system design: finding an optimal components’ architecture (sensor and actuator placement), modelling the system, analysing the system’s model properties (robustness, observability, controllability, diagnosability), design control, fusion and estimation algorithms.