Toward Supervision of Stochastic System-of- Systems Engineering: A Multi-Level Hypergraph Approach

System-of-systems (SoS) face major challenges, including heterogeneity, scalability, and intricate interactions among component systems (CSs). These systems typically operate in dynamic environments, introducing uncertainty and stochastic behavior. Many existing studies tend to oversimplify these complexities, with limited research focusing on supervising SoS under such conditions. Graph models, such as hypergraphs (HG), have been effective in modeling SoS organizations, while stochastic and weighted hypergraphs have been successfully used to handle stochasticity in other complex systems. In this article, we present the Multi-Level Stochastic Hypergraph (MLSHG) model, designed to address the challenges of modeling stochastic SoS. We also propose a novel algorithm for supervising large-scale SoS, integrating bottom-up monitoring with top-down reconfiguration to detect the addition or failure of CSs and manage the overall system’s capacity to achieve long-term objectives. In a case study on a mushroom harvesting SoS, the results showed that incorporating stochastic elements with an adaptive threshold enabled early reconfiguration, reducing deviations from the final goal. Additionally, the capability-based reconfiguration approach exhibited low computational time, with performance scaling linearly with the number of CSs, thus enhancing the system’s scalability.