Analytical construction of relay dynamic system point mappings taking into account delays

Abstract

The article considers solving the problem of analytical construction of Poincare maps for finding simple and complex limit cycles in a relay dynamic system involving constant perturbation and delay. Application of Neymark’s theory of multivariate point transformations allows reducing the problem under consideration to the search for a multifold fixed point thus overcoming the difficulty of finding complex periodic motions. The choice of switching lines as arcs without contact taking into account delays significantly simplified the task of analytical construction of point mapping. The results of analytical constructions are confirmed by numerical simulation of movements. The results obtained can find practical application in developing reactive systems for controlling the orientation and stabilization of the spacecraft. Compared with the previously known solution, a more complete result is obtained, which is of particular importance in the study of systems with high efficiency of executive bodies.