Cyber-physical systems are self-adaptive, changing their behavior at run time to adapt to their context. Hence, their simulations must also handle variability at run time. The lack of support for variability in industrial equation-based modeling languages, such as Modelica, causes problems when simulating self-adaptive systems, e.g., they only limitedly support structural variability, and state transitions are based on if-then-else conditions that can cause conflicts, especially for complex control mechanisms. We present a modeling technique for equation-based models containing variability by implementing concise and dedicated language constructs to express state space and transitions via contextual modeling. Contextual modeling abstracts the modeled world and allows the definition of constraints that reduce the risk of reaching conflicting states. We demonstrate the feasibility of our approach on a case study, presenting the advantages of our modeling technique regarding the definition of state control and the reduction of risk for reaching conflicting states.

Context-aware systems are crucial in modern cyber-physical systems (CPS), enabling dynamic adaptation to changing conditions. Many such systems involve complex variability. Modelica, a leading equation-based language for modeling and simulating physical systems, struggles to manage this complexity. As variability management becomes more complex, traditional Modelica constructs such as conditional statements, state machines, and state graphs become increasingly inadequate and difficult to maintain. This work introduces a context-oriented modeling paradigm for Modelica by integrating Petri Net-based context control with FMI-based Variable Structure Systems (VSS). Specifically, we present Context Petri Nets (CoPN) as a formal mechanism for representing and managing contextual dependencies. By combining CoPN with VSS, our approach enables advanced variability management, supporting the modeling and simulation of complex, context-aware CPS.