An optimal control model for a system of degenerate parabolic integro-differential equations. (English. Russian original) Zbl 1190.49003
Cybern. Syst. Anal. 43, No. 6, 838-847 (2007); translation from Kibern. Sist. Anal. 2007, No. 6, 90-102 (2007).
Summary: An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. Sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions.
MSC:
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 35J99 | Elliptic equations and elliptic systems |
| 49M30 | Other numerical methods in calculus of variations (MSC2010) |
Keywords:
optimal control; system of integro-differential equations; parabolic equation; degenerate parabolicity; existence and uniqueness of solutions; stable numerical solutionReferences:
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