The applicability of methodologies that could be used for the design and operation of complex systems (CPS, mechatronics, product-process, etc.) depends on the existence of a formal framework that ensures their consistency, pertinence and reliability.

These rigorous formalisms are mainly based on :

• The mathematics of complex systems, such as connective structures, category theory, topological analysis, etc.
• Computer concepts such as formal languages, multi-agent systems, data mining, etc.

Coupled with new design methodologies, they permit :

• structuring and implementing a digital twin that integrates a large number of heterogenous models ;
• ensuring and maintaining the consistency of the necessary models ;
• managing the diversity of modelling languages and tools used during the design phase. We can mention :
• Formal modelling languages (Modelica, Altarica) and semi-formal ones (SysML) ;
• Dedicated tools such as Matlab, Cameo Systems Modeler, Capella-Arcadia, PTC Integrity Modeler, AnyLogic, 3D Experience, ModelCenter, Karren, etc.