In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated by simulations.
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The purpose of this paper is to show for parabolic systems how one can achieve a final gradient in a subregion w of the system domain W. First, we give a definition and delineate some properties of this new concept, and then we introduce the concept of regionally gradient strategic actuators. The importance of the spatial structure and location of the actuators in achieving regional gradient controllability is emphasized. Consequently, we concentrate on the determination of a control which would realize a given final gradient on w with minimum energy. The developed approach is original and leads to numerical algorithms for constructing optimal controls. This approach is also illustrated by an example.
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