Abstract
The aim of the present paper is to derive a recursive formula of state estimation for a parabolic differential system with a “partially unknown input.” Here the word “partially” unknown input means that the input term of the system is a product of two functions: one is a known function of time variable and of spatial variable; the other is an unknown function of spatial variable. It is desired to perform the state estimation by identifying the latter function. The formula is derived applying the results of J. L. Lions for the decoupling of Riccati type.
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