ToPSyS research group deals with tolerance, prognosis and design of cyber-physical system of systems through an integrated approach. It includes modeling, analysis of the properties of the model of a dynamic system (observability, controllability, diagnosability, reconfigurability), analysis of the properties of the model of a managerial system (independence, dispersion, cooperation, evolution) and the design of monitoring, prognosis and control algorithms, in order to make dynamic systems and cyber-physical system of systems fault tolerant. We consider nonlinear continuous dynamic systems (represented by differential equations and graphical formalisms), discrete event dynamic systems, hybrid dynamic systems (switching systems), dynamic systems with discrete events) and cyber-physical systems of systems (represented by multi-level formalisms, based on graphs or on differential algebra). The algorithms are described to control and supervise the system to another level of abstraction in normal operation, but also in situations where certain components are faulty and disrupt the performance and missions of the system. Our objective is therefore to guarantee a certain level of operational safety (availability, reliability, security, maintainability) by setting up a supervision system, which includes monitoring, requirements, data fusion, mode management, reconfiguration , prognosis and automatic control, thus allowing to better tolerate these failures at the scale of a single cyber-physical system up to an organization of a system of cyber-physical systems.