Optimum control of parabolic system with the distributed parameters on the graph

V. V. Provotorov

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2014), pp. 154-163

Résumé

The initial and regional task for the parabolic equation with distributed is considered parameters on limited graph $\Gamma$ and it the corresponding problem of optimum control. Work continues researches of the author in the direction of existence and uniqueness optimum control in a case, when a condition of differential system an essence display of a piece of $[0,T]$ ($T<\infty$) in special space. Thus in quality of space of managements the space of functions integrated with a square is used $L_2(\Gamma_T)$, $\Gamma_T=\Gamma\times(0,T)$. Bibliogr. 13.

Détail

Keywords: initial and regional task with the distributed parameters on the graph, the generalized decision, optimum control.

Bibliographie

[1] Provotorov V. V., “Creation of boundary managements in a task about clearing of fluctuations of system of strings”, Vestnik St. Petersburg University, ser. 10: Applied mathematics, computer science, control processes, 2012, no. 1, 62–71

[2] Provotorov V. V., Gnilitsky Yu. A., “Boundary management of wave system in space of the generalized decisions on the graph”, Vestnik St. Petersburg University, ser. 10: Applied mathematics, computer science, control processes, 2013, no. 3, 112–120

[3] Provotorov V. V., “Decomposition on own functions of a problem of Storm Liouville on the graph bunch”, Izv. vyssh. ucheb. zavedenij. Mathematica, 2008, no. 3, 50–62

[4] Provotorov V. V., “Spectral task on the graph with a cycle”, Differential equations, 46:11 (2010), 1665–1666

[5] Provotorov V. V., Makhinova O. A., Regional tasks for the equations with the distributed parameters on graphs, Scientific book, Voronezh, 2013, 133 pp.

[6] Volkova A. S., Gnilitskaya Yu. A., Provotorov V. V., “About resolvability of regional tasks for the equations of parabolic and hyperbolic types on the geometrical count”, Control systems and information technologies, 2013, no. 1 (51), 11–15

[7] Lions J.-L., Optimum control of the systems described by the equations with private derivatives, Per. s fr. N. H. Rozova, ed. R. V. Gamkrelidze, Mir, M., 1972, 414 pp.

[8] Aleksandrov A. Yu., Zhabko A. P., “About asymptotic stability of solutions of one class of systems of the nonlinear differential equations with delay”, Izv. vyssh. ucheb. zavedenij. Mathematica, 2012, no. 5, 3–12

[9] Veremey E. I., Sotnikova M. V., “Plasma stabilization on the basis of the forecast with steady linear approach”, Vestnik St. Petersburg University, ser. 10: Applied mathematics, computer science, control processes, 2011, no. 1, 116–133

[10] Zhabko N. A., “Parametrical identification of dynamic models of sea vessels”, Vestnik of the Voronezh. State techn. un-ty, 8:1 (2012), 80–84

[11] Karelin V. V., “Penal functions in a problem of management of supervision process”, Vestnik St. Petersburg University, ser. 10: Applied mathematics, computer science, control processes, 2010, no. 4, 109–114

[12] Podvalny S. L., Plakhotnyuk O. S., Multiple modeling of dynamic systems of evolutionary type for management in extreme situations, Izd-vo Voronezh. gos. tehn. un-ta, Voronezh, 2007, 171 pp.

[13] Podvalny S. L., Management information systems of monitoring of difficult objects, Nauchnaya kniga, Voronezh, 2010, 164 pp.