This article is cited in 2 papers

Applied mathematics

Method for finding a solution to a linear nonstationary interval ODE system

A. V. Fominyh<sup>ab

a</sup> Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy pr. V. O., St. Petersburg, 199178, Russian Federation
^b St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. On the basis of these conditions, the method of the steepest descent is applied to the original problem. Some numerical examples illustrate the constructed algorithm realization.

Keywords: linear nonstationary interval system of ordinary differential equations, differential inclusion, support function, the steepest descent method.

UDC: 517.926.7+517.977.58

MSC: 34B05, 49M05

Received: November 29, 2020
Accepted: April 5, 2021

Language: English

DOI: 10.21638/11701/spbu10.2021.205