Piecewise constant control of linear mechanical systems in the general case

I. M. Alesova, L. K. Babadzanjanz, A. M. Bregman, K. M. Bregman, I. Yu Pototskaya, Yu Yu Pupysheva, A. T. Saakyan

Research outputpeer-review

1 Citation (Scopus)

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 equal to the total area of all steps of all control components ("Expenditure criteria"). In the absence of control, the solution of the system is equal to the sum of the components (frequency components) corresponding to different eigenvalues of the matrix of the 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 Expenditure criteria, is proposed.

Original languageEnglish
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017
EditorsCharalambos Tsitouras, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos
PublisherAmerican Institute of Physics
Volume1978
ISBN (Electronic)9780735416901
DOIs
Publication statusPublished - 10 Jul 2018
EventInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 - Thessaloniki
Duration: 25 Sep 201730 Sep 2017

Conference

ConferenceInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017
CountryGreece
CityThessaloniki
Period25/09/1730/09/17

Fingerprint

linear systems
eigenvalues
moments
coefficients
matrices

Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Alesova, I. M., Babadzanjanz, L. K., Bregman, A. M., Bregman, K. M., Pototskaya, I. Y., Pupysheva, Y. Y., & Saakyan, A. T. (2018). Piecewise constant control of linear mechanical systems in the general case. In C. Tsitouras, T. Simos, T. Simos, T. Simos, T. Simos, & T. Simos (Eds.), International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 (Vol. 1978). [100009] American Institute of Physics. https://doi.org/10.1063/1.5043753
Alesova, I. M. ; Babadzanjanz, L. K. ; Bregman, A. M. ; Bregman, K. M. ; Pototskaya, I. Yu ; Pupysheva, Yu Yu ; Saakyan, A. T. / Piecewise constant control of linear mechanical systems in the general case. International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017. editor / Charalambos Tsitouras ; Theodore Simos ; Theodore Simos ; Theodore Simos ; Theodore Simos ; Theodore Simos. Vol. 1978 American Institute of Physics, 2018.
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Alesova, IM, Babadzanjanz, LK, Bregman, AM, Bregman, KM, Pototskaya, IY, Pupysheva, YY & Saakyan, AT 2018, Piecewise constant control of linear mechanical systems in the general case. in C Tsitouras, T Simos, T Simos, T Simos, T Simos & T Simos (eds), International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017. vol. 1978, 100009, American Institute of Physics, Thessaloniki, 25/09/17. https://doi.org/10.1063/1.5043753

Piecewise constant control of linear mechanical systems in the general case. / Alesova, I. M.; Babadzanjanz, L. K.; Bregman, A. M.; Bregman, K. M.; Pototskaya, I. Yu; Pupysheva, Yu Yu; Saakyan, A. T.

International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017. ed. / Charalambos Tsitouras; Theodore Simos; Theodore Simos; Theodore Simos; Theodore Simos; Theodore Simos. Vol. 1978 American Institute of Physics, 2018. 100009.

Research outputpeer-review

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AB - 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 equal to the total area of all steps of all control components ("Expenditure criteria"). In the absence of control, the solution of the system is equal to the sum of the components (frequency components) corresponding to different eigenvalues of the matrix of the 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 Expenditure criteria, is proposed.

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Alesova IM, Babadzanjanz LK, Bregman AM, Bregman KM, Pototskaya IY, Pupysheva YY et al. Piecewise constant control of linear mechanical systems in the general case. In Tsitouras C, Simos T, Simos T, Simos T, Simos T, Simos T, editors, International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017. Vol. 1978. American Institute of Physics. 2018. 100009 https://doi.org/10.1063/1.5043753