## 1 Introduction  
Control of complex interconnected systems has a wide range of usage in our society. Some applications can be found in [1, 2] (fault diagnosis), [3] (unmanned vehicles), [4, 5] (scheduling problems), [6, 7] (hydraulic networks), [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] (power systems, mechanical systems), [22, 23] (processing plants and supply chain management), [24] (Biological systems), and [25, 26, 27] (Information processing). For instance, control and fault diagnosis of large-scale interconnected networks are tasked with some design challenges due to each network's particular characteristics. An engineer designing a control or fault diagnosis scheme for such systems considers the number of equations and variables involved in the process and its complexity due to non-linearities [28]. Mature energy prediction models, mainly Building Energy Modelling and Manufacturing Process Simulation, have been used extensively in their respective fields. However, they use different methods for each part of a building or a process, limiting the ability of the used frameworks to identify energy and yield improvements. Similarly, a holistic approach, such as in co-simulation (see below), \"is more likely to achieve the greatest energy efficiency savings or reduction in energy use\" [29; 30]. In particular, the food sector is of great interest as there are many aspects that can be addressed through numerical models. [PERSON] et al., 2021 [9] published a comprehensive review regarding the numerical modeling of food products and the numerical simulation of food processes. They conclude that there are few examples of dynamic modeling and simulation of food processes that vary rapidly and unpredictably over time; for some types of processes, the authors propose the use of techniques typically used in other engineering fields. In fact, food processes are very complex and difficult to model. On the other hand, they are well represented by models used for the dynamic simulation of interconnected systems. Moreover, \"deviations in the proper operation of these interconnected systems or their parts are no longer merely technical difficulties; they pose a danger with a global security impact\" [31]. These drawbacks are repetitively developed each time for the systems to be controlled and simulated, especially in the food industry. Another difficulty arises when dealing with extensive interconnected systems, such as the global iterative method, which is necessary to simulate non-linear systems and slow down the simulation process due to the huge computational work [32]. These systems are typically used in food and food processing modelling [9], such as biogas production from food processing residues [11; 13], pasta factories [12; 17], food freezing facilities, and installed cogeneration plants [14]. In contrast, one of the main advantages of modelling complex systems as interconnected ones are the facility of substituting one of the subsystems with an updated version. Even its portability characteristic allows substituting with a black box, furnished by another company. In this latter case, it is not appropriate to change the solving algorithms because the equations modelling the new subsystem are not known at worst. In fact, in this case, the black box model makes it hard to use any benefits from the knowledge of the governing equations. What has just been said allows us to state that the techniques used in many engineering applications can be effectively exported to food applications, such as in the whole food supply chain. In all these cases, we find a common aspect: the presence of interconnected systems. In general, there is a lack of literature about the application of interconnected systems modelling to the food industry because of the lack of efficient algorithms needed.