COMPUTATION OF STACKELBERG TRAJECTORIES IN A CLASS OF TWO-PERSON LINEAR DIFFERENTIAL GAMES WITH TERMINAL PLAYERS' PAYOFFS AND POLYGONAL CONSTRAININGS FOR CONTROLS

摘要

The report suggests a numerical method for constructing Stackelberg trajectories in a linear two-person n-dimensional differential game with terminal payoffs of players and polygonal constrainings for controls. Formalization of players' strategies in the game is based on formalization and the results of positional antagonistic differential games theory, developed by N. N. Krasovskii and his scientific school. The game is reduced to a game on the plane and the problem is transformed to solving a non-standard optimal control problem. For the approximation of the trajectories sets for this problem a set of computational geometry algorithms in plane is used, including convex hull construction, union and intersection of polygons and a Minkowski sum for polygons.