Interval observer design and control of uncertain non-homogeneous heat equations

Tatiana Kharkovskaia, Denis Efimov, Emilia Fridman, Andrey Polyakov, Jean Pierre Richard

Research output: Contribution to journalArticlepeer-review


The problems of state estimation and observer-based control for heat non-homogeneous equations under distributed in space point measurements are considered. First, an interval observer is designed in the form of Partial Differential Equations (PDEs), without Galerkin projection. Second, conditions of boundedness of the interval observer solutions with non-zero boundary conditions and measurement noise are proposed. Third, the obtained interval estimates are used to design a dynamic output-feedback stabilizing controller. The advantages of the PDE-based interval observer over the approximation-based one are clearly shown in the numerical example.

Original languageEnglish
Article number108595
StatePublished - Jan 2020


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