Solution of the Two-Level Hierarchical Minimax Program Control Problem in a Nonlinear Discrete-Time Dynamical System⁎

Abstract

In this paper we consider a discrete-time dynamical system consisting of two controllable objects. The dynamics of each object is described by the corresponding nonlinear discrete-time vector recurrent equation. The quality of process implementation at each level of the control system is estimated by the corresponding terminal convex and differentiable functional. For the dynamical system under consideration, a mathematical formalization of a two-level hierarchical minimax program 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 and convex mathematical programming problems, and a finite discrete optimization problems. © 2018