Optimal Control of Solutions to the Showalter - Sidorov Problem for the Sobolev Type Equation of Higher Order

被引:0
|
作者
Zamyshlyaeva, A. A. [1 ]
Tsyplenkova, O. N. [1 ]
Bychkov, E., V [1 ]
机构
[1] South Ural State Univ, Chelyabinsk, Russia
关键词
Sobolev type equations; strong solutions; optimal control;
D O I
暂无
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The theory of dynamical measurements is a wide and independent part of the metrology. Previously, dynamical measurements were studied mostly within the framework of inverse problems theory. Lastly there arose a new idea for the restoration of dynamically distorted signals, which evolved into a theory of optimal measurements. It was suggested to use methods of optimal control theory for the Sobolev type equations in solving this problem of dynamical measurements. In this article, a problem of optimal control of solutions of the Sobolev type equation of higher order with the Showalter - Sidorov condition is studied. All considerations are held under assumption of relative polynomial boundedness of an operator pencil. The theorem stating that there exists a unique strong solution to abstract equation with the Showalter - Sidorov condition is proved. The sufficient and necessary (in the case when infinity is a removable singularity of the A-resolvent of an operator pencil) conditions for existence of unique optimal control for strong solutions are found. We use the ideas and methods developed by G.A. Sviridyuk and his disciples.
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页数:4
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