Superellipsoidal Approximations in the Speed-in-action Problem for a Two-dimensional Linear Discrete System with Bounded Control

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Abstract

The paper considers a two-dimensional linear discrete system with bounded control. For the system, the problem of speed is solved, that is, the construction of a control process that transfers the system from the initial state to the origin in the minimum number of steps. If the set of acceptable control values has a superellipse structure, then the problem of calculating optimal control can be reduced to solving a system of algebraic equations. A superellipsoidal approximation method has been developed for sets of arbitrary structure. Examples are considered in the paper.

General Information

Keywords: linear control system, speed problem, 0-controllability sets, maximum principle, superellipse

Journal rubric: Optimization Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2023130209

Received: 25.04.2023

Accepted:

For citation: Ibragimov D.N., Podgornaya V.M. Superellipsoidal Approximations in the Speed-in-action Problem for a Two-dimensional Linear Discrete System with Bounded Control. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2023. Vol. 13, no. 2, pp. 151–179. DOI: 10.17759/mda.2023130209. (In Russ., аbstr. in Engl.)

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Information About the Authors

Danis N. Ibragimov, PhD in Physics and Matematics, Associate Professor of the Department of Probability Theory and Computer Modeling, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0001-7472-5520, e-mail: rikk.dan@gmail.com

Violetta M. Podgornaya, Master's Student, Engineer at the Department of Probability Theory and Computer Modeling, Moscow Aviation Institute (National Research University) (MAI), Moscow, Russia, ORCID: https://orcid.org/0009-0004-9956-3002, e-mail: vita1401@outlook.com

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