Сonstructing of attainability domains for a class of nonsmooth control systems on the plane

Recieved: 09/19/2023

Accepted: 12/19/2023

Published: 04/02/2024

Keywords: control system, attainability domain, Pontryagin’s maximum principle, numerical methods, Kaldor’s model of business cycle

To cite this article

Aseev A. S., Samsonov S.P. Сonstructing of attainability domains for a class of nonsmooth control systems on the plane. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2024. N 2, p.6-17 https://doi.org/10.55959/MSU/0137-0782-15-2024-47-2-6-17.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Aseev A. S. (Lomonosov Moscow State University (MSU))
Samsonov S.P. (Lomonosov Moscow State University (MSU))

Abstract

A method for approximate construction of the boundary of attainability domain is developed for a class of nonsmooth controlled dynamical systems on the plane that arise in economics. The method is based on an explicit procedure for smoothing the system and using the apparatus of the Pontryagin maximum principle. As an example, we consider the problem of constructing the boundary of the attainability domain for a controlled version of the well-known Kaldor’s model of business cycle.