In the first part of the talk we present a new approach to state observation,
called Parameter Estimation-based Observers (PEBO) whose main idea is to translate
the state estimation problem into one of estimation of constant, unknown parameters.
The class of systems for which is applicable is identified via two assumptions
related to the transformability of the system into a suitable cascaded form and our
ability to estimate the unknown parameters. The first condition involves the
solvability of a partial differential equation while the second one requires
some persistency of excitation-like conditions. We present also PEBO in a unified
framework together with the - by-now classical - Kasantzis-Kravaris-Luenberger
and Immersion and Invariance observers. In the second part we show that, for systems for which
a linear regression-like relation is available, it is possible to combine PEBO with a new
estimation technique called Dynamic Regressor Extension and Mixing (DREM).
This new technique, called DREMBAO, is used to generate adaptive observers.
PEBO and DREMBAO are shown to be applicable to position estimation of a class
of electromechanical systems - including motors and MagLev
systems - and for speed observation of a class of mechanical systems.
The performance of these observers is compared with high-gain and sliding mode observers.
As expected, it is shown that - in the presence of noise - the performance
of the two latter designs is significantly below par with respect to the other techniques.
Parameter estimation and gradient descent-based observers: application to mechanical and electromechanical systems
Session Chair: Michael Ruderman