Email this article Optimization of the Reachable Set of a Linear System with Respect to Another Set
- Authors: Balashov M.V.1, Kamalov R.A.1
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Affiliations:
- Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
- Issue: Vol 63, No 5 (2023)
- Pages: 739-759
- Section: ОПТИМАЛЬНОЕ УПРАВЛЕНИЕ
- URL: https://journals.rcsi.science/0044-4669/article/view/136131
- DOI: https://doi.org/10.31857/S004446692305006X
- EDN: https://elibrary.ru/PJPZUE
- ID: 136131
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Abstract
Given a linear controlled autonomous system, we consider the problem of including a convex compact set in the reachable set of the system in the minimum time and the problem of determining the maximum time when the reachable set can be included in a convex compact set. Additionally, the initial point and the time at which the extreme time is achieved in each problem are determined. Each problem is discretized on a grid of unit vectors and is then reduced to a linear programming problem to find an approximate solution of the original problem. Additionally, error estimates for the solution are found. The problems are united by a common ideology going back to the problem of finding the Chebyshev center.
About the authors
M. V. Balashov
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
Email: balashov73@mail.ru
117997, Moscow, Russia
R. A. Kamalov
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
Author for correspondence.
Email: balashov73@mail.ru
117997, Moscow, Russia
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