On bounded control construction in a game-theoretic problem of controlling the angular motion of an asymmetric solid

A game-theoretic approach to the problem of the reorientation of an asymmetric solid in the presence of uncontrollable interference is described. The approach reducing this nonlinear problem to a linear game-theoretic problem is presented in Vorotnikov (1994, 1995). The method is based on a specific choice of the structural form of control rules. Prescribed “geometric constraints” on the control functions are taken into account. Verification of such constraints requires calculations in the state set of auxiliary linear conflict-controlled systems. The nonlinear control rules obtained in this way are robust and ensure that the body arrives at the prescribed state in a finite time, which can be computed within the framework of the proposed solution scheme starting from the time-optimization requirement