Title | The Riccati-type equation in the optimal control synthesis problem for a differential system with distributed parameters on the graph |
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Authors | V. V. Provotorov^{1}^{1}Voronezh State University |

Annotation | There is synthesis with distributed parameters perfomed on the graf (inverse relationship) for solving the problem of optimal distributed control of parabolic system with distributed parameters: the optimal control is determined through the state of the system. The state of the system is determined by the weak solution of the initial-boundary value problem for the parabolic equation, the control effect on the system and the observation of its state are performed throughout the graph and the entire time interval. Generalization of the Kalman results, known for the finite-demensional case, was obtained on bounded operators for evolution systems with distributed parameters showing on the graph. The used methods are fundamental for the study of optimal control problems in the dynamics of laminar flows of multiphase media. |

Keywords | parabolic system with distributed parameters on the graph, weak solutions, optimal control synthesis problem |

Citation | Provotorov V. V. ''The Riccati-type equation in the optimal control synthesis problem for a differential system with distributed parameters on the graph '' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 498-510. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper68.pdf. - Date of access: 05.12.2020. |

**© SVMO, National Research Mordovia State University, 2020**

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