M19 – ISTANBUL 25/04/2016 – 29/04/2016

Convergence theory for observers

Laurent Praly

Abstract of the course


Observers are objects delivering estimation of variables which cannot be directly measured. The access to such "hidden" variables is made possible by combining modeling and measurements. But this is bringing face to face real world and its abstraction with as a result the need for dealing with uncertainties. The corresponding theoretical observers are consequently very complex, multivalued and often extremely difficult to implement. This implies that approximations and simplifications are involved with, as a consequence, convergence problems.


As introduction we state the observation problem in its full generality and mentionn possible theoretical answers. This shows that an observer is nothing but a dynamical system with measurements as inputs and estimates as outputs. We restrict ourselves with the case where this system is finite dimensional and when there is no uncertainty. We concentrate our attention on the convergence aspect with first giving necessary condition and then sufficient conditions. Particular emphasis is given to general purpose observers as high gains observers and nonlinear Luenbergerobservers.