Block Coordinate Descent Method in the Problem of the Fastest Transition into a Given Area for Linear Discrete Systems

Abstract

In the paper, we construct a numerical solution to the problem of the fastest possible transfer of the state of a linear discrete-time system from a given initial position into a predetermined ellipsoid around the origin. Our algorithmic approach is based on the method of block coordinate descent. As the main result we formulate and prove the convergence theorem for the proposed algorithm.