Seminar Details
2023-03-21 (14h) : Towards a Unified Perspective to Observer Design
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Pauline Bernard (Mines Paris)
Abstract :
We start by reviewing the main techniques of state observer design for continuous-time dynamical systems. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show that each class of observer relies on transforming the system dynamics into a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Then, we give a particular focus to the theory of KKL or nonlinear Luenberger observers. This design consists in looking for a change of coordinates changing the system dynamics into a contracting filter of the output. A state estimate is then obtained by implementing this filter from any initial condition and left-inverting the transformation, which is shown to be possible under a very weak backward-distinguishability property. We show how, unlike other methods, this idea is universal and can be extended to any type of dynamical systems (continuous or discrete time, autonomous or discrete, observable or non-observable, etc), thus offering a promising road towards a unified paradigm for observer design.