## 3 Materials and Methods  
The life cycle cost (LCC) of any system includes both the initial investment costs for development and production, and the operating costs over the life of the system. When building an LCC model, it is necessary to consider the interdependence of all factors, in which changes in one factor can have a significant impact on the overall LCC of the system. Applied to non-life support systems, this LCC model can be used to calculate combinations of autonomous systems with both fully renewable resources and delivery by cargo spacecrafts, as well as to evaluate trade-offs between different life support systems in terms of cost and sustainability. In the LCC model of life support systems for autonomous transport systems with crews, it is necessary to take into account various functional components:  
* The complexity of the life support system, including the number and variety of components, can have a significant impact on the cost of the system. * The degree of autonomy of the system, including the number and complexity of automated functions, can also affect the cost of the system. * The technology and materials used in the life support system can impact its cost, particularly if cutting-edge or specialized technologies are required. * The scale of production, including the number of units to be produced and the level of investment required for production, can also impact the cost of the system. * Development costs, including the cost of design, engineering, testing, and certification, can have a significant impact on the overall cost of the system. * The ongoing costs of maintenance and operation, including spare parts, repairs, and replacement, should also be considered in the cost model. * The duration of the mission, including the length of time the life support system will be in operation, can also impact the cost of the system. Let us consider one of the approaches to the construction of this LCC model, taking into account most of these factors. Table 2 shows the main notation used in constructing the model equations. \begin{table}
\begin{tabular}{c c l} \hline \hline
**Notations** & **Parameters** \\ \hline \(T_{m}\) & - & Autonomous vehicle mission time \\ \(\gamma\) & - & Volume of life support resources (LSRs) consumption by the crew for 1 day \\ \(s_{1}\) & - & Cost of LSRs consumed by crew members in one day \\ \(\Omega=\Omega_{A}+\Omega_{\overline{A}}\) & - & LSS architecture that fully meets the needs of the LSRs crew \\ \(\Omega_{A}\) & - & On-board component of the LSS architecture, autonomously meeting the needs of the LSRs crew on the vehicle through their reproduction \\ \(\Omega_{\overline{A}}\) & - & A component of the LSS architecture, the resources generated which must be replenished externally. \\ \(\eta=\Omega_{A}/\Omega\) & - & Degree of autonomy of LSS \\ \(C_{\Xi}(\Omega,t)\) & - & LSS Life Cycle Cost \\ \(C_{\eta}(\Omega,t)\) & - & Cost of development and production of LSS architecture with a degree of autonomy \(\eta\) \\ \(C_{r}(\Omega,t)\) & - & The cost of delivery of external LSRs not generated on board the transport system of the autonomous component of the LSS architecture during the mission \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notations used in the model. The assessment of the efficiency of the life support systems (LSSs) for the mentioned autonomous transport system is based on the evaluation of the total cost throughout its life cycle:  
\[C(\Omega,t)=C_{\eta}(\Omega,t)+C_{r}(\Omega,t)+C_{m}(\Omega,t) \tag{1}\]  
We frame the challenge of designing the architecture for the life support system in an autonomous transport system as the development of an LSS with an optimal architecture, denoted as \(\Omega_{opt}\). The objective is to minimize the total cost incurred over the mission duration \(T_{m}\):  
\[C\big{(}\Omega_{opt},t\big{)}=min\big{\{}(C(\Omega,t)|t=T_{m})\big{\}} \tag{2}\]  
There are three alternative LSS architectures for the examined ecosystem:  
* Open LSS (OLSS).