Interval observers design for hybrid and biological systems

Kwassi Holali Degue 1
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : This work deals with interval observer design techniques. In the first part, the problem of interval observer design is studied for a class of linear hybrid systems. Several observers are proposed oriented on different conditions of positivity and stability for estimation error dynamics. Efficiency of the proposed approach is demonstrated by computer experiments for academic and bouncing ball systems. Note that interval observer design techniques for linear hybrid systems have been developed for the first time in the present work. The second part is devoted to the interval estimation of sequestred infected erythrocytes in plasmodium falciparum malaria patients. An advantage of the interval approaches in this case is that they give a bound of the errors at any time, which can be controlled in order to ensure the positivity of the state estimates of the system. Thus, interval estimation is very close to the reality in this case and has not been developed before the present work. An interval observer in order to estimate the sequestered parasite population is proposed in this report. Its efficiency is demonstrated by computer simulations.
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Kwassi Holali Degue. Interval observers design for hybrid and biological systems. Automatic. 2015. ⟨hal-01542615⟩

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