Section: Overall Objectives

Objectives

The ALIEN project aims at designing new real-time estimation algorithms. Within the huge domain of estimation, ALIEN addresses the following, particular trends: software-based reconstruction of unmeasured variables (also called "observation"), filtering of noisy variables, estimation of the n -th order time derivatives of a signal, parametric estimation of a linear/nonlinear model (including delay and hybrid systems).

The novelty lies in the fact that ALIEN proposes algebra-based methods, leading to algorithms that are fast (real-time is aimed at), deterministic (noise is considered as a fast fluctuation), and non-asymptotic (finite-time convergence). This is why we think that ALIEN's studies are shedding a new light on the theoretical investigations around estimation and identification. As it was told, estimation is a huge area. This explains the variety of possible application fields, which both concern signal processing and real-time control. Several cooperations have already been launched on various concrete industrial problems with promising results.

Let us briefly mention some topics which will be studied in this project. In automatic control, we will be dealing with:

• identifiability and identification of uncertain parameters in the system equations, including delays;

• estimation of state variables, which are not measured;

• fault diagnosis and isolation;

• observer-based chaotic synchronization, with applications in cryptography and secure systems.

A major part of signal and image processing is concerned with noise removal, i.e., estimation. Its role in fundamental questions like signal modeling, detection, demodulation, restoration, (blind) equalization, etc, cannot be overestimated. Data compression, which is another key chapter of communication theory, may be understood as an approximation theory where well chosen characteristics have to be estimated. Decoding for error correcting codes may certainly also be considered as another part of estimation. We know moreover that any progress in estimation might lead to a better understanding in other fields like mathematical finance or biology.