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This article is cited in 2 scientific papers (total in 2 papers)
Optimal control
Optimization of the reachable set of a linear system with respect to another set
M. V. Balashov, R. A. Kamalov Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997, Moscow, Russia
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.
Key words:
reachable set, uniform convexity, condition of nonempty interior, multivalued integral, linear programming, approximation in the Hausdorff metric.
Received: 02.11.2022 Revised: 21.11.2022 Accepted: 02.02.2023
Citation:
M. V. Balashov, R. A. Kamalov, “Optimization of the reachable set of a linear system with respect to another set”, Zh. Vychisl. Mat. Mat. Fiz., 63:5 (2023), 739–759; Comput. Math. Math. Phys., 63:5 (2023), 751–770
Linking options:
https://www.mathnet.ru/eng/zvmmf11550 https://www.mathnet.ru/eng/zvmmf/v63/i5/p739
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