Abstract

In this paper, we consider a class of economic dynamics models in the form of linear functional differential systems with continuous and discrete times (hybrid models) that covers many kinds of dynamic models with aftereffect. The focus of attention is periodic boundary value problems with deviating argument, control problems with respect to general on-target vector-functional and questions of stability to solutions. For boundary value problems, some sharp sufficient conditions of the unique solvability are obtained. The attainability of on-target values is under study as applied to control problems with polyhedral constraints with respect to control, some estimates of the attainability set as well as estimates to a number of switch-points of programming control are presented. For a class of hybrid systems, a description of asymptotic properties of solutions is given.

Highlights

  • In the context of the digitalization of the economy, strengthening the scientific validity of decisions is becoming more and more relevant

  • We consider some of the typical problems of economic dynamics in relation to a wide class of hybrid dynamic models with aftereffect

  • A model governing the dynamics of the system under consideration can be written in the form of functional differential system (FDS) with continuous and discrete times (Hybrid FDS = HFDS, for short)

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Summary

Introduction

In the context of the digitalization of the economy, strengthening the scientific validity of decisions is becoming more and more relevant The basis of such strengthening is economic and mathematical methods that implement a targeted approach to solving actual applied problems. A model governing the dynamics of the system under consideration can be written in the form of functional differential system (FDS) with continuous and discrete times (Hybrid FDS = HFDS, for short). It should be noted that in most cases dynamics in continuous time is governed by ordinary differential systems. For a class of hybrid systems, a description of asymptotic properties of solutions is presented

Preliminaries
From the AFDE Theory
Hybrid System as an AFDE
Periodic Boundary Value Problems
Integral Restrictions on Functional Operators
Point-Wise Restrictions on Functional Operators
A Nonlinear Case
Control Problems
General Results
Constrained Control of Hybrid Systems with Discrete Memory
An Example
Stability and Asymptotic Behavior of Solutions
The Case of Two Scalar Equations
A Case of Periodic Parameters
Discussion

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