On two non-asymptotic estimation methods
报告题目: On two non-asymptotic estimation methods

which cannot be measured. Moreover, the measurements usually contain noises. Sometime,
fast estimations with convergence in finite-time are required in on-line applications.
For these reasons, the modulating functions method introduced by Shinbrot in 1954 and
the algebraic parametric estimation method introduced by Fliess and Sira-Ramirez in 2003
both originally for system identification have been applied and extended in signal processing
and automatic control, such as parameter estimation and numerical differentiation, etc.
The two methods have the following advantages. Firstly, the obtained estimators are exactly
given by integral formulae of the observation signal. Thus, they are algebraic and non-asymptotic.
Fast estimation can be provided using sliding integration window with finite length. The
knowledge of initial conditions is not needed and the derivatives of noisy signals don't need
to be calculated. Moreover, thanks to the integrals in the formulae, they are robust with
respect to corrupting noises without the need of knowing in priori their statistical properties.
Recently, these methods have been extended to fractional order systems. In this talk, the
ideas of these two methods will be explained by giving simples examples. Moreover, the
applications to parameter estimation and numerical differentiation will be presented.

in 2005 and 2007, respectively. He earned his Ph.D. degree in Applied Mathematics with great
honors from University of Lille 1 & INRIA Lille-Nord Europe in October 2011. He was a
postdoctoral fellow in Arts et Métiers ParisTech during October-December 2011.
From January 2012 to November 2013, he was a postdoctoral fellow at King Abdullah University
of Science and Technology (KAUST) in Saudi Arabia. Currently, he is a tenured Assistant
Professor in INSA (French National Institute of Applied Sciences) Centre Val de Loire, where he
belongs to Control Team in PRISME Laboratory. Dr. Liu’s main research interests concern with
estimation and identification for integer order and fractional order systems, such as numerical
differentiation and parameter estimation. Until now, he has published more than 40 papers in
international journals and conferences such as IEEE Transactions on Automatic Control,
Automatica, SIAM Journal on Scientific Computing and Systems & Control Letters, etc. Thanks
to his Ph.D. work, he earned the Chinese Government award for outstanding self-financed
students abroad in 2012. Moreover, his Ph.D. student Xing Wei also earned this award in 2017.