Minimization of energy costs for UAV management in a conflict task

This article considers the method of developing an evader control strategy in the non-linear differential pursuit-evasion game problem. It is assumed that the pursuer resorts to the most probable control strategy in order to capture the evader and that at each moment the evader knows its own and the enemy’s physical capabilities. This assumption allows to bring the game problem down to the problem of a unilateral evader control, with the condition of reaching a saddle point not obligatory to be fulfilled. The control is realised in the form of synthesis and additionally ensures that the requirements for bringing the evader to a specified area with terminal optimization of certain state variables are satisfiedt. The solution of this problem will significantly reduce the energy losses for controlling an unmanned vehicle, the possible effect is to save 15-20 % of fuel with a probability of 0.98, to solve the problem of chasing the enemy.

ε-Positional Strategies in the Theory of Differential Pursuit Games and the Invariance of a Constant Multivalued Mapping in the Heat Conductivity Problem

In this paper, we consider two problems. In the first problem, we prove that if the assumption from the paper [1] and one additional condition on the parameters of the game hold, then the pursuit can be finished in any neighborhood of the terminal set. To complete the game, an ε-positional pursuit strategy is constructed.In the second problem, we study the invariance of a given multivalued mapping with respect to the system with distributed parameters. The system is described by the heat conductivity equation containing additive control terms on the right-hand side.