Seminar Details
2010-11-02 (15.00) : Geometrical methods in observer design : observers and symmetries
At Euler building
Organized by Mathematical Engineering
Speaker :
Bonnabel, Silvère
Abstract :
Observers compute a real-time estimation of the state of a dynamical
system from several sensor's (noisy) measurements. Most famous observers are the Luenberger observer and the Kalman filter,
both of them having been designed for
linear systems. For systems described by non-linear differential
equations, there is no general method to design observers. In this talk,
we propose to focus on a special class of nonlinear systems : systems
possessing symmetries (or invariances). For those systems we propose a
general method to build candidate observers which respect the
symmetries. For instance the conservation laws involved in the models of
chemical reactors are independent of the choice of physical units (mol,
kg, ...). In this case, the method allows to find all observers which
are also invariant to a change of units. We will apply the method to the
example of multisensor fusion for mobile vehicles, in which the
symmetries are the Galilean invariances.
The theory only deals with a limited number of symmetries (for instance
a change of physical units). At the end of the talk, we will also
consider the problem of designing a velocity observer for conservative
Lagrangian systems with configuration (position) measurements, invariant
to all possible change of coordinates (infinite number of symmetries).
We will use the Jacobi metric, and we will view the Lagrangian dynamics
of a conservative system as a geodesic flow on a manifold. This work is
based on the paper by Aghannan and Rouchon (IEEE-TAC, 2003).