On periodic solution to control problem with time-driven switching

Dmitry Gromov; Anton Bondarev; Ekaterina Gromova

doi:10.1007/s11590-021-01749-6

On periodic solution to control problem with time-driven switching

Dmitry Gromov
, Anton Bondarev
, Ekaterina Gromova^*

^*Corresponding author for this work

Department of Economics

St. Petersburg State University
RAS - Krasovskii Institute of Mathematics and Mechanics, Ural Branch
Higher School of Economics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this contribution, we consider the optimal control problem for a switched dynamical system. While such systems can exhibit rather complex behavior in the case of only one switch, the most interesting problem corresponds to the case, when the system undergoes an infinite number of switches. We study the limiting behavior of optimal solutions under such assumption and show that there are three types of solutions, two of which correspond to cyclic evolution of the system state and control.

Original language	English
Pages (from-to)	2019-2031
Number of pages	13
Journal	Optimization Letters
Volume	16
Issue number	7
DOIs	https://doi.org/10.1007/s11590-021-01749-6
Publication status	Published - 19 May 2021

Keywords

Hybrid optimal control
Optimal control
Periodic system
Switched dynamics

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10.1007/s11590-021-01749-6

Cite this

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abstract = "In this contribution, we consider the optimal control problem for a switched dynamical system. While such systems can exhibit rather complex behavior in the case of only one switch, the most interesting problem corresponds to the case, when the system undergoes an infinite number of switches. We study the limiting behavior of optimal solutions under such assumption and show that there are three types of solutions, two of which correspond to cyclic evolution of the system state and control.",

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AU - Bondarev, Anton

AU - Gromova, Ekaterina

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Y1 - 2021/5/19

N2 - In this contribution, we consider the optimal control problem for a switched dynamical system. While such systems can exhibit rather complex behavior in the case of only one switch, the most interesting problem corresponds to the case, when the system undergoes an infinite number of switches. We study the limiting behavior of optimal solutions under such assumption and show that there are three types of solutions, two of which correspond to cyclic evolution of the system state and control.

AB - In this contribution, we consider the optimal control problem for a switched dynamical system. While such systems can exhibit rather complex behavior in the case of only one switch, the most interesting problem corresponds to the case, when the system undergoes an infinite number of switches. We study the limiting behavior of optimal solutions under such assumption and show that there are three types of solutions, two of which correspond to cyclic evolution of the system state and control.

KW - Hybrid optimal control

KW - Optimal control

KW - Periodic system

KW - Switched dynamics

UR - https://www.scopus.com/pages/publications/85106224769

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JO - Optimization Letters

JF - Optimization Letters

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ER -

On periodic solution to control problem with time-driven switching

Abstract

Keywords

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