Application of an Intelligent Control on Economics Dynamic System: The Attractive Invariant Ellipsoid Approach

摘要

In this paper, we explore the application of attractive ellipsoid methodology (Poznyak et al. in Attractive ellipsoids in robust control. Springer, Berlin, 2014) on a new demand and supply model. The balance between the demand and supply is expressed by the Lin and Yang model (Li and Yang in Int J Bifurc Chaos 27(01):1750016, 2017), described by differential equations, even if in the such a demand-supply model, other factors change and have significant effect on demand-supply dynamics. Analysis is compared with the situation when the prices of most products do not stay close to their equilibrium values and the Li and Yang demand and supply model is described by both ordinary differential equation and differential algebraic equation system. To achieve a specific economic goal, we will be able to design a management strategy based on minimum size of the invariant attractive ellipsoid, associated with the dynamic system, with a good performance in the rejection of external disturbances. We can consider a new transformed problem instead of the original problem with respect to solvability and related questions. Theoretical results are illustrated by an example.