The article substantiates and proves the necessity of developing mathematical support for existing and prospective models of weapons and military equipment, namely, class I unmanned aerial systems, for flight optimization and control using unmanned aerial vehicle-based repeaters, which are used to solve the tasks of information and reconnaissance support of troops (forces) of the Armed Forces of Ukraine. It is established that the use of such systems provides information and fire superiority over the enemy during aerial reconnaissance, engagement of their forces and assets, etc. Based on these prerequisites, the paper presents a formalized statement of an important scientific problem, which consists in increasing the efficiency of class I unmanned aerial systems by optimizing the flight route, network topology, us well us energy-efficient control using unmanned aerial vehicle-based repeaters. The authors define "Unmanned aerial systems efficiency" as a comprehensive indicator of multi-criteria optimization of a non-linear compromise scheme, which depends on the values of the complex's probability of being hit, its combat radius, and survivability. A structural and logical scheme of the research is presented, which includes the solution of the following subtasks: analysis of the use of tactical class I unmanned aerial systems, unmanned aerial vehicle-based repeaters, and their routing methods, as well as methods of planning optimal flight routes based on transport problem solving algorithms; optimization of the flight route of class I unmanned aerial systems to bypass their engagement zones; energy-efficient use of tactical unmanned aerial systems based on repeaters. The final scientific result is the developed mathematical support for class I unmanned aerial systems and the verification of its performance. The presented structural and logical scheme allows to systematize the essence and content of the scientific research.
Humeniuk et al. (2025) studied this question.