Numerical Solution of an Optimal Control Problem for One Linear Hoff Model Defined on Graph

In this paper an optimal control over solutions of a one no classical mathematical physics problem for linear Hoff equations defined on a finite oriented connected graph has been investigated. This one we reduced to the initial-finish value problem for an abstract Sobolev type equation by special selected functional spaces. Existence and uniqueness for strong solution of the initial-finish value problem for a linear Sobolev type equation was established. It is shown that in this case exist a unique optimal control over solutions of considered problem. The obtained abstract results are applied to the one linear Hoff model defined on graph and existence and uniqueness for solution of this problem was established. This work contains a numerical experiment based on obtained theoretical results. For constructing of the approximate solution we used Galerkin's method. Also in this paper we used ideas and methods developed by G.A. Sviridyuk and his pupils.

Keywords

sobolev type equations, the initial-finish value problem, optimal control, the linear Hoff equation.

References

1. Zagrebina S.A. The Multipoint Initial-finish Problem for Hoff Linear Model. Bulletin of South Ural State University. Seria "Mathematical Modelling, Programming & Computer Software", 2012, no. 5 (264), issue 11, pp. 4-12. (in Russian)
2. Sviridyuk G.A., Fedorov V.E. Linear Sobolev Type Equations and Degenerate Semigroups of Operators. Utrecht, Boston, Koln, Tokyo, VSP, 2003.
3. Shestakov A.L., Sviridyuk G.A. Optimal Measurement of Dynamically Distorted Signals. Bulletin of South Ural State University. Seria "Mathematical Modelling, Programming & Computer Software", 2011, no. 17(234), issue 8, pp. 70-75.
4. Manakova N.A., Dylkov A.G., On one optimal control problem with a penalty functional in general form. Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2011, issue 4(25), pp. 18-24. (in Russian)