Superellipsoidal Approximations in the Speed-in-action Problem for a Two-dimensional Linear Discrete System with Bounded Control

Abstract

The paper considers a two-dimensional linear discrete system with bounded control. For the system, the problem of speed is solved, that is, the construction of a control process that transfers the system from the initial state to the origin in the minimum number of steps. If the set of acceptable control values has a superellipse structure, then the problem of calculating optimal control can be reduced to solving a system of algebraic equations. A superellipsoidal approximation method has been developed for sets of arbitrary structure. Examples are considered in the paper.