Boundary control of an unstable heat equation via measurement of domain-averaged temperature. (English) Zbl 1006.93039

The authors have designed a feedback boundary controller for an unstable heat equation. The equation models a thin rod with heat loss to a surrounding medium and with heat generation inside the rod. The heat generation adds a destabilizing linear term on the right-hand side of the equation.
The boundary control is designed in the form of an integral operator with a known, continuous kernel function and can be interpreted as a backstepping control law.


93C20 Control/observation systems governed by partial differential equations
93D15 Stabilization of systems by feedback
35K05 Heat equation
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