Control of mechanical systems by the mixed "time and expenditure" criterion

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Abstract

The optimal controlled motion of a mechanical system, that is determined by the linear system ODE with constant coefficients and piecewise constant control components, is considered. The number of control switching points and the heights of control steps are considered as preset. The optimized functional is combination of classical time criteria and "Expenditure criteria", that is equal to the total area of all steps of all control components. In the absence of control, the solution of the system is equal to the sum of components (frequency components) corresponding to different eigenvalues of the matrix of the ODE system. Admissible controls are those that turn to zero (at a non predetermined time moment) the previously chosen frequency components of the solution. An algorithm for the finding of control switching points, based on the necessary minimum conditions for mixed criteria, is proposed.

Original languageEnglish
Title of host publication8th Polyakhov's Reading
Subtitle of host publicationProceedings of the International Scientific Conference on Mechanics
EditorsElena V. Kustova, Gennady A. Leonov, Mikhail P. Yushkov, Nikita F. Morosov, Mariia A. Mekhonoshina
PublisherAmerican Institute of Physics
ISBN (Electronic)9780735416604
DOIs
StatePublished - 2 May 2018
EventInternational Scientific Conference on Mechanics: 8th Polyakhov's Reading - Saint Petersburg, Russian Federation
Duration: 29 Jan 20182 Feb 2018

Publication series

NameAIP Conference Proceedings
Volume1959
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Scientific Conference on Mechanics: 8th Polyakhov's Reading
CountryRussian Federation
CitySaint Petersburg
Period29/01/182/02/18

Scopus subject areas

  • Physics and Astronomy(all)

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