Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 39 | |
Number of page(s) | 26 | |
DOI | https://doi.org/10.1051/cocv/2024028 | |
Published online | 03 May 2024 |
Method for Finding Solution to Nonsmooth Differential Inclusion of Special Structure
1
Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, 61 Bolshoy pr. V.O., St. Petersburg 199178, Russian Federation
2
St.Petersburg University, 7–9 Universitetskaya nab., St.Petersburg 199034, Russian Federation
* Corresponding author: alexfomster@mail.ru
Received:
16
March
2023
Accepted:
26
March
2024
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in phase coordinates) functions. It is required to find a trajectory that would satisfy differential inclusion with the boundary conditions prescribed and simultaneously lie on the surface given. Such problems arise in practical modeling discontinuous systems and in other applied ones. The initial problem is reduced to a variational one. It is proved that the resulting functional to be minimized is superdifferentiable. The necessary minimum conditions in terms of superdifferential are formulated. The superdifferential (or the steepest) descent method in a classical form is then applied to find stationary points of this functional. Herewith, the functional is constructed in such a way that one can verify whether the stationary point constructed is indeed a global minimum point of the problem. The convergence of the method proposed is proved. The method constructed is illustrated by examples.
Mathematics Subject Classification: 34A60 / 49J52 / 49K05
Key words: Differential inclusion / support function / superdifferential
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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