The application of applied category theory to quantify mission success

Mission engineering is the quantification of the effects applied by a system of systems to achieve measurable desired results. The execution of the mission is defined by a mission thread; that is the sequence of actions/processes executed by elemental systems. The domain of complex missions has been described as “wicked” because traditional military and space program-based systems engineering practices fail due to a lack of discrete phases, a dependence on context, and the non-uniqueness of a “good-enough” mission thread. Wicked problems also tend to be unstructured (non-hierarchical) with no centralized control and do not lend themselves to linear step-by-step processes. Wicked problems are inherently uncertain leading to the broader issue of trust across a mission knowledge base, and any mission level analyses. Wicked problems are also characterized and challenged by combinatoric complexity. Mission success is primarily driven by the interrelationships between systems and not just by the individual systems themselves. The success of mission engineering will require an iterative approach of modeling, simulation, and analysis resulting in a continuous reduction in uncertainty and refinement in the topology of the mission thread. OODA-based decomposition of mission threads focused on Boyd’s Orient function provides focus on system interrelationships. Trust provides decision-maker confidence in the results that has proved elusive to traditional validation approaches. The approach described in this paper is based upon using applied category theory as a basis for building mission threads, mission models, data stores, and integrating simulation ensembles.