Identification adaptative de système à un automate hybride dans le contexte des jumeaux numériques Cyber-Physiques

In the era of Cyber-Physical Systems (CPS) and digital twins, the dynamic and precise modeling of complex systems has become a crucial necessity in many industrial sectors. Digital twins, which are true virtual replicas of physical systems, require models capable of simultaneously capturing the continuous dynamics and discrete switches that are characteristic of hybrid systems. However, identifying these systems presents a major challenge, particularly when they need to adapt to system changes in real time while maintaining high levels of fidelity and genericity. This thesis proposes an innovative method for adaptive identification of hybrid systems, specifically designed to meet the demands of digital twins in industrial environments. Unlike traditional approaches, this method stands out by adopting a non-sequential approach to the identification sub-problems, fostering a more flexible resolution framework and optimizing a global cost function. This process ensures the model's fidelity to the real system while guaranteeing its generality across various application scenarios. The first chapter sets the context for the work, defining the key concepts of CPS and digital twins, and outlining the specific challenges of identifying hybrid systems. The second chapter focuses on existing work in the field of hybrid automata identification and highlights their limitations in the context of this research. Chapters three and four develop an innovative methodological approach, combining fidelity metrics based on the distance between signals and genericity measures derived from formal language theory. This approach leads to a global optimization of the identification process, integrating fidelity and genericity constraints while ensuring an adaptive approach. The proposed method is then tested in the final chapters on several theoretical and practical cases, ranging from academic theoretical systems to real industrial applications, such as the control of a storage unit from Schneider Electric. These tests demonstrate that the method is robust in the face of complex systems and capable of evolving according to observed changes in the physical system. The results also show its performance improvement compared to existing methods, particularly in managing complex hybrid dynamics and the structure of the identified automaton. This work thus offers an innovative approach to developing digital twins, emphasizing the flexibility, precision, and adaptability required in modern industrial environments. It is intended for researchers, engineers, and industry professionals seeking to design hybrid system models to optimize the digital twins of industrial cyber-physical systems.