The toreador problem (Q1316694)

This paper is devoted to the pursuit-evasion problem on the plane with 3 objects, with fixed end time and with information noises. The first object (target) is treated as stationary one and lies in the origin of \(R^ 2\). The second (evader) moves to the origin according to a given linear differential equation from the given initial state and his goal is to retain the motion of the third one outwards a given ball with radius \(R\), centered at the origin. The third one (pursuer) moves toward the evader according to a rule of simple pursuit with given intensity. It is assumed that the second object is controllable. Using the construction of so-called stable bridges, due to Krasovskij and Sobbotin, the authors propose a numerical procedure for the solution of the evasion problem described above. The procedure of control with a guide is described and some results of a computer simulation are presented.