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Stabilization of a heat-ODE system cascaded at a boundary point and an intermediate point. (English) Zbl 1386.93262

Summary: This paper considers the stabilization of a heat-ODE system cascaded at a boundary point and an intermediate point. The stabilizing feedback control law is designed by the backstepping method. Based on a novel transformation, we prove that all the kernel functions in the forward and inverse transformations are of the class \(C^2\). Moreover, the effectiveness of controller design is shown with a numerical simulation. Finally, we show the coherence between the controllability assumption of the main theorem in this paper and the known one for a special case with \(\lambda=0\).

MSC:

93D21 Adaptive or robust stabilization
93D20 Asymptotic stability in control theory
93C20 Control/observation systems governed by partial differential equations
93C15 Control/observation systems governed by ordinary differential equations
35K10 Second-order parabolic equations
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