Abstract
In this paper controllability and observability analysis are performed for the heat flow on the state-space of one dimension. The process is described by a semilinear parabolic partial differential equation. We report that the associated linear infinite-dimensional operator is a Riesz-spectral operator and generates a C0-semigroup of bounded linear operators. Then we construct a sufficient and necessary condition for the approximate controllability and observability of the system. In particular, a finite number of dominant modes of the system are approximately observable when the input is measured at the heat output by an appropriate sensor.
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