Analysis of a game problem of braking a disk in the case of constant controls

Abstract

The process of braking a disk in the form of a differential game is studied. The dynamic system is based on the Coulomb friction model. The existence of a game value in the case of constant controls of the players is analyzed for different values of initial velocities and parameters of the disk. The aim is to minimize the braking distance. For each case, the guarantees of the first and second players are examined, and a statement about the existence or nonexistence of a game value is formulated. For example, it is shown that in the case of slip-free braking, there exists a game value, and it is attained when the first player applies the greatest possible control allowing him not to slip and the second player minimizes the friction. In the conclusion of the paper, we prove a final theorem stating that the slip-free mode is the best braking mode for the first player under constant controls. © 2019 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.