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Interval observer design and control of uncertain non-homogeneous heat equations. (English) Zbl 1430.93080
Summary: 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.

MSC:
93B53 Observers
93C20 Control/observation systems governed by partial differential equations
35K05 Heat equation
93D15 Stabilization of systems by feedback
93D25 Input-output approaches in control theory
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