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ON THE PROPERTIES OF THE SOLVABILITY SET FOR A LINEAR SYSTEM WITH UNCERTAINTY
- Authors: Melnikova A.A1,2, Tochilin P.A1,3, Daryin A.N1
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Affiliations:
- Lomonosov Moscow State University
- V.A. Trapeznikov Institute of Control Sciences of RAS
- Issue: Vol 60, No 11 (2024)
- Pages: 1484-1498
- Section: CONTROL THEORY
- URL: https://ter-arkhiv.ru/0374-0641/article/view/649593
- DOI: https://doi.org/10.31857/S0374064124110054
- EDN: https://elibrary.ru/JEGHXR
- ID: 649593
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Abstract
The work is devoted to the problem of verifying that the state of a linear controlled system of differential equations will hit the target set over a finite time interval, despite the uncertainties (noise). Some geometric, pointwise convex constraints on uncertainties are imposed. In the case of a two-dimensional state space a method is proposed for constructing a solvability set without the calculation of the convex hulls of the functions necessary to construct a support function of the geometric difference of the sets. A Hamilton–Jacobi–Bellman type equation is obtained, which is satisfied by the distance function to the solvability set.
About the authors
A. A Melnikova
Lomonosov Moscow State University;
Email: nastya.a.melnikova@gmail.com
P. A Tochilin
Lomonosov Moscow State University; V.A. Trapeznikov Institute of Control Sciences of RAS
Email: tochilin@cs.msu.ru
A. N Daryin
Lomonosov Moscow State University
Email: daryin@mail.ru
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