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



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


Received: 25.04.2023


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, Senior Lecturer, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID:, e-mail:

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:, e-mail:



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