Algorithm for Solving of Two-Level Hierarchical Minimax Adaptive Control Problem in a Linear Discrete-Time Dynamical System

Abstract

In this paper we consider a discrete-time dynamical system consisting from two controllable objects. The dynamics of each object is described by the corresponding vector linear discrete-time recurrent relation. In this dynamical system there are two levels of control. The quality of process implementation at each level of the control system is estimated by the corresponding terminal linear functional. For the dynamical system under consideration, a mathematical formalization of a two-level hierarchical minimax adaptive control problem in the presence of perturbations, and an algorithm for its solving are proposed. The construction of this algorithm can be implemented as a finite sequence of solutions of a linear mathematical programming problems, and a finite discrete optimization problems. © 2018