Optimal synthesis in the problem of impulsive correction of motion

A minimax problem of correcting the motion of a dynamic system acted upon by perturbing forces of restricted magnitude is considered. The corrective action is carried out in the form of impulsive control, with a restriction on the total magnitude of the impulses and their number. This formulation models the problem of the impulsive correction of motion of an aircraft acted upon by external perturbations. The problem represents, in fact, a differentially-impulsive game /1/ in which the player controlling the correction aims to secure for himself a guaranteed minimum of the terminal functional. Following the methods used in /2/ we construct, for the problem with isotropic dynamics, an optimal synthesis of the correction instances. The present paper touches on the work done in /3–5/.