The small parameter method in the optimisation of a quasi-linear dynamical system problem
| Autor: | Anatoly I. Kalinin, Leonid I. Lavrinovich, Darya Y. Prudnikova |
|---|---|
| Jazyk: | Belarusian<br />English<br />Russian |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Журнал Белорусского государственного университета: Математика, информатика, Iss 2, Pp 23-33 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2520-6508 2617-3956 |
| DOI: | 10.33581/2520-6508-2022-2-23-33 |
| Popis: | We consider an optimisation problem for the transient process in a quasi-linear dynamical system (contains a small parameter at non-linearities) with a performance index that is a linear combination of energy costs and the duration of the process. An algorithm for constructing asymptotic approximations of a given order to the solution of this problem is proposed. The algorithm is based on the asymptotic decomposition by integer powers of a small parameter of the initial values of adjoint variables and the duration of the process that are finite-dimensional elements, according to which the solution of the problem is easily restored. The computational procedure of the algorithm includes solving the problem of optimising the transient process in a linear dynamical system, integrating systems of linear differential equations, and finding the roots of non-degenerate linear algebraic systems. We also show how the constructed asymptotic approximations can be used to construct optimal control in the problem under consideration for a given value of a small parameter. |
| Databáze: | Directory of Open Access Journals |
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