Minimax stabilization of the line-of-sight of an inertial object on a moving base in the presence of friction force

Abstract

The solution of the problem of optimal stabilization of the line-of-sight of an inertial object in the vicinity of the program trajectory is given. The motion of this line is described by a system of nonlinear differential equations of the fourth order. The system of equations is linearized in the vicinity of the desired motion mode. In the problem solved, the perturbations are represented as deviations of the initial position from zero, as well as in the form of constant perturbations. The stabilization is carried out by means of linear feedback. In the problem, the feedback coefficients are calculated as optimal for the worst possible disturbances. Calculations are performed in two ways: a search of all possible combinations of parameters with a given sampling step and a parallel genetic algorithm.