Algorithm for solving of two-level hierarchical minimax program terminal control problem for nonlinear discrete-time dynamical system in the presence of external perturbations

Abstract

In this paper we consider a controlled dynamical system consisting of two objects in the presence of external perturbations. 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 linear and nonlinear discrete-time recurrent vector equations. In the system under consideration there are two levels of control: basic level (the level I) that is dominant level and auxiliary level (the level II) that is subordinate level. The quality of the control process on every level of the control system is estimated by corresponding convex terminal functional. Both the control levels have different informational and control connections defined in advance. In this paper we study the problem of optimization of guaranteed result for program control the final state of phase vectors of the objects in the presence of external perturbations. For this problem we propose a mathematical formalization of two-level hierarchical minimax program control the final state of the dynamical system in the presence of external perturbations and incomplete information. In this paper for solving of the investigated problem is proposed the algorithm that has a form of a recurrent procedure of solving a linear and a convex mathematical programming problems, and a finite optimization problems.