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Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory. / Dodonov, V. V.; Soltakhanov, Sh Kh; Tovstik, Petr Evgenievich; Yushkov, Mikhail Petrovich; Zegzhda, Sergey Andreevich.

Foundations in Engineering Mechanics. Springer Nature, 2021. p. 249-322 (Foundations in Engineering Mechanics).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Dodonov, VV, Soltakhanov, SK, Tovstik, PE, Yushkov, MP & Zegzhda, SA 2021, Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory. in Foundations in Engineering Mechanics. Foundations in Engineering Mechanics, Springer Nature, pp. 249-322. https://doi.org/10.1007/978-3-030-64118-4_6

APA

Dodonov, V. V., Soltakhanov, S. K., Tovstik, P. E., Yushkov, M. P., & Zegzhda, S. A. (2021). Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory. In Foundations in Engineering Mechanics (pp. 249-322). (Foundations in Engineering Mechanics). Springer Nature. https://doi.org/10.1007/978-3-030-64118-4_6

Vancouver

Dodonov VV, Soltakhanov SK, Tovstik PE, Yushkov MP, Zegzhda SA. Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory. In Foundations in Engineering Mechanics. Springer Nature. 2021. p. 249-322. (Foundations in Engineering Mechanics). https://doi.org/10.1007/978-3-030-64118-4_6

Author

Dodonov, V. V. ; Soltakhanov, Sh Kh ; Tovstik, Petr Evgenievich ; Yushkov, Mikhail Petrovich ; Zegzhda, Sergey Andreevich. / Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory. Foundations in Engineering Mechanics. Springer Nature, 2021. pp. 249-322 (Foundations in Engineering Mechanics).

BibTeX

@inbook{9accb449ec60461abe128933abfbd0ae,
title = "Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory",
abstract = "This chapter consists of two parts. In the first part we present two theories of motion of nonholonomic systems with high-order (program) constraints. In the first theory, we construct a consistent system of differential equations for the unknown generalized coordinates and the Lagrange multipliers. The second theory is based on the generalized Gauss principle. In the second part, for one of the most principal problems of the control theory-the problem of optimal control force that transforms a given mechanical system in a given amount of time from one phase state into a different one–we employ the second theory. This allows one to construct a control force in the form of a polynomial of time. The application of this theory is illustrated on the model problem of oscillation suppression for a cart with pendulums. We pose and solve an extended boundary-value problem. Because of this, it proves possible to find a control force without jumps peculiar to solutions obtained via the Pontryagin maximum principle.",
author = "Dodonov, {V. V.} and Soltakhanov, {Sh Kh} and Tovstik, {Petr Evgenievich} and Yushkov, {Mikhail Petrovich} and Zegzhda, {Sergey Andreevich}",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",
year = "2021",
doi = "10.1007/978-3-030-64118-4_6",
language = "English",
series = "Foundations in Engineering Mechanics",
publisher = "Springer Nature",
pages = "249--322",
booktitle = "Foundations in Engineering Mechanics",
address = "Germany",

}

RIS

TY - CHAP

T1 - Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory

AU - Dodonov, V. V.

AU - Soltakhanov, Sh Kh

AU - Tovstik, Petr Evgenievich

AU - Yushkov, Mikhail Petrovich

AU - Zegzhda, Sergey Andreevich

N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - This chapter consists of two parts. In the first part we present two theories of motion of nonholonomic systems with high-order (program) constraints. In the first theory, we construct a consistent system of differential equations for the unknown generalized coordinates and the Lagrange multipliers. The second theory is based on the generalized Gauss principle. In the second part, for one of the most principal problems of the control theory-the problem of optimal control force that transforms a given mechanical system in a given amount of time from one phase state into a different one–we employ the second theory. This allows one to construct a control force in the form of a polynomial of time. The application of this theory is illustrated on the model problem of oscillation suppression for a cart with pendulums. We pose and solve an extended boundary-value problem. Because of this, it proves possible to find a control force without jumps peculiar to solutions obtained via the Pontryagin maximum principle.

AB - This chapter consists of two parts. In the first part we present two theories of motion of nonholonomic systems with high-order (program) constraints. In the first theory, we construct a consistent system of differential equations for the unknown generalized coordinates and the Lagrange multipliers. The second theory is based on the generalized Gauss principle. In the second part, for one of the most principal problems of the control theory-the problem of optimal control force that transforms a given mechanical system in a given amount of time from one phase state into a different one–we employ the second theory. This allows one to construct a control force in the form of a polynomial of time. The application of this theory is illustrated on the model problem of oscillation suppression for a cart with pendulums. We pose and solve an extended boundary-value problem. Because of this, it proves possible to find a control force without jumps peculiar to solutions obtained via the Pontryagin maximum principle.

UR - http://www.scopus.com/inward/record.url?scp=85120855162&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-64118-4_6

DO - 10.1007/978-3-030-64118-4_6

M3 - Chapter

AN - SCOPUS:85120855162

T3 - Foundations in Engineering Mechanics

SP - 249

EP - 322

BT - Foundations in Engineering Mechanics

PB - Springer Nature

ER -

ID: 92421505