### 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 language | English |
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Title of host publication | International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 |

Editors | Charalambos Tsitouras, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos |

Publisher | American Institute of Physics |

Volume | 1978 |

ISBN (Electronic) | 9780735416901 |

DOIs | |

Publication status | Published - 10 Jul 2018 |

Event | International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 - Thessaloniki Duration: 25 Sep 2017 → 30 Sep 2017 |

### Conference

Conference | International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 |
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Country | Greece |

City | Thessaloniki |

Period | 25/09/17 → 30/09/17 |

### Fingerprint

### Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017*(Vol. 1978). [100009] American Institute of Physics. https://doi.org/10.1063/1.5043753

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*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.

Research output › › peer-review

TY - GEN

T1 - Piecewise constant control of linear mechanical systems in the general case

AU - Alesova, I. M.

AU - Babadzanjanz, L. K.

AU - Bregman, A. M.

AU - Bregman, K. M.

AU - Pototskaya, I. Yu

AU - Pupysheva, Yu Yu

AU - Saakyan, A. T.

PY - 2018/7/10

Y1 - 2018/7/10

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85047176395&partnerID=8YFLogxK

U2 - 10.1063/1.5043753

DO - 10.1063/1.5043753

M3 - Conference contribution

VL - 1978

BT - International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017

A2 - Tsitouras, Charalambos

A2 - Simos, Theodore

A2 - Simos, Theodore

A2 - Simos, Theodore

A2 - Simos, Theodore

A2 - Simos, Theodore

PB - American Institute of Physics

ER -