The Average Sentinel of the Heat Equation with an Unknown Reaction

Abstract

In this paper, we analyze the identification of the amount of pollutant discharged problem by each source in a heat system when the dynamics of the state are governed by a parameterized unknown operator. In this way, we introduce the notion of average sentinel. The decomposition method is used to solve the equation of this problem, the gradient method is used to calculate the averaged control, and the combination of the two methods is used to estimate the pollution terms. Numerical example is given to confirm this result.

Keywords

• average sentinel
• identification method
• averaged observability
• pollution term
• decomposition method
• gradient method