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**Motion control of a rotor with a cavity with a viscous fluid.**
*(English.
Russian original)*
Zbl 1126.93039

Autom. Remote Control 68, No. 2, 284-295 (2007); translation from Avtom. Telemekh. 68, No. 2, 81-94 (2007).

Summary: A formulation and solution procedure of optimal control problems for perturbed relative uniform motion of a body with a cavity filled with a viscous incompressible fluid are proposed. In this paper, the case with a cylinder is considered; however, this approach is basically true for a cavity of an arbitrary form. The formula for the angular velocity of perturbed motion depending on an external perturbing element is devised. After that, we have a possibility to set different optimal control problems and apply the formalism elaborated in the optimal control theory. Two illustrated problems are given.

### MSC:

93C73 | Perturbations in control/observation systems |

76D55 | Flow control and optimization for incompressible viscous fluids |

76U05 | General theory of rotating fluids |

49N90 | Applications of optimal control and differential games |

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\textit{A. A. Gurchenkov} et al., Autom. Remote Control 68, No. 2, 284--295 (2007; Zbl 1126.93039); translation from Avtom. Telemekh. 68, No. 2, 81--94 (2007)

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### References:

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[8] | Gurchenkov, A.A., Esenkov, A.S., and Tsurkov, V.I., Motion Control of a Rotor with a Cavity Filled with an Ideal Fluid. II, Teor. Sist. Upravlen., 2006, no. 3, pp. 82–89. · Zbl 1260.49075 |

[9] | Gurchenkov, A.A., Vikhrevye dvizheniya zhidkosti v polosti vrashchayushchegosya tela (Rotational Fluid Motion in the Cavity of a Rotating Body), Moscow: Narodnyi Uchitel’, 2001. |

[10] | Ishmukhametov, A.Z., Regularized Approximate Methods of Projection and Conditional Gradient with Finite-Stage Internal Algorithms, Dokl. Ross. Akad. Nauk, 2003, vol. 390, no. 3. · Zbl 1083.47504 |

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