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

Bošković, Dejan M.; Krstić, Miroslav; Liu, Weijiu

IEEE Trans. Autom. Control 46, No. 12, 2022-2028 (2001).

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.

Reviewer: Sebastian Aniţa (Iaşi)

MSC:

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

Keywords:

stabilization; feedback boundary controller; unstable heat equation; backstepping