Algorithm for solving of two-level hierarchical minimax adaptive control problem in a nonlinear discrete-time dynamical system

Abstract

In this article we consider a discrete-time dynamical system consisting from two controllable objects. The dynamics of the first object (the main object of the system) and the second object (the auxiliary object of the system) are described respectively by nonlinear and linear discrete-time recurrent vector equations. In this dynamical system there are two levels of control. The quality of process implementation at first and second levels of the control system are estimated by the terminal convex and linear functionals respectively. 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 and a convex mathematical programming problems, and a finite discrete optimization problems, and operations on a convex sets. © 2019 Author(s).