The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.
In this work, we introduce and examine the notion of domination for a class of linear distributed systems. This consists in studying the possibility to make a comparison between input or output operators. We give the main algebraic properties of such relations, as well as characterizations of exact and weak domination. We also study the case of actuators, and various situations are examined. Applications and illustrative examples are also given. By duality, we extend this study to observed systems....
We consider a discrete disturbed system given by the difference bilinear equation where are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function. Let be a tolerance index on the output. The disturbance is said to be -admissible if, where is the output signal associated with the case of an uninfected system. The set of all -admissible disturbances is the admissible set. The characterization of is investigated and numerical...
We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.
In this paper we show how to find convenient boundary actuators, termed boundary efficient actuators, ensuring finite-time space compensation of any boundary disturbance. This is the so-called remediability problem. Then we study the relationship between this remediability notion and controllability by boundary actuators, and hence the relationship between boundary strategic and boundary efficient actuators. We also determine the set of boundary remediable disturbances, and for a boundary disturbance,...
The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion...
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