Optimization of the Reachable Set of a Linear System with Respect to Another Set

M. V. Balashov; Балашов М. В.; R. A. Kamalov; Камалов Р. А.

doi:10.31857/S004446692305006X

Optimization of the Reachable Set of a Linear System with Respect to Another Set

Authors: Balashov M.V.¹, Kamalov R.A.¹
Affiliations:
1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
Issue: Vol 63, No 5 (2023)
Pages: 739-759
Section: Optimal control
URL: https://ruspoj.com/0044-4669/article/view/664849
DOI: https://doi.org/10.31857/S004446692305006X
EDN: https://elibrary.ru/PJPZUE
ID: 664849

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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.

Keywords

reachable set, uniform convexity, condition of nonempty interior, multivalued integral, linear programming, approximation in the Hausdorff metric

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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