Finite-time simultaneous parameter and state estimation using modulating functions

This paper discusses the use of techniques related to the modulating function method for performing joint parameter and state estimation. After a short review of other methods related to modulating functions, we look at observability issues and the so-called Least-Squares observers to extend currently existing results on joint parameter and state estimation using modulating functions. An example is given as illustration.

[1]  Taous-Meriem Laleg-Kirati,et al.  Robust fractional order differentiators using generalized modulating functions method , 2015, Signal Process..

[2]  Alexander Medvedev.  Continuous least-squares observers with applications , 1996, IEEE Trans. Autom. Control..

[3]  Sridhar Ungarala,et al.  Batch scheme recursive parameter estimation of continuous-time systems using the modulating functions method , 1997, Autom..

[4]  Ganti Prasada Rao,et al.  Identification of lumped linear systems in the presence of unknown initial conditions via Poisson moment functionals , 1980 .

[5]  Anuradha M. Annaswamy,et al.  Robust Adaptive Control , 1984, 1984 American Control Conference.

[6]  Tzyh Jong Tarn,et al.  Observability of Nonlinear Systems , 1973, Inf. Control..

[7]  F. Fairman,et al.  Identification in the presence of initial conditions , 1972 .

[8]  A. Pearson,et al.  On the identification of polynomial input-output differential systems , 1985 .

[9]  Alexander Medvedev,et al.  Directional sensitivity of continuous least-squares state estimators , 2010, Syst. Control. Lett..

[10]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[11]  Olivier Gibaru,et al.  Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs , 2014 .

[12]  Marcin Nowak,et al.  The Quality of Identification for Different Normalizations of Continuous Transfer Functions , 2003, Modelling, Identification and Control.

[13]  K.S.P. Kumar,et al.  On the observability of nonlinear systems: I , 1971 .

[14]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[15]  J. Loeb,et al.  More about process identification , 1965 .

[16]  Heinz A. Preisig,et al.  Theory and application of the modulating function method—I. Review and theory of the method and theory of the spline-type modulating functions , 1993 .

[17]  H. Freud.  Mathematical Control Theory , 2016 .

[18]  H. Unbehauen,et al.  Identification of continuous-time systems , 1991 .

[19]  Johann Reger,et al.  On algebraic time-derivative estimation and deadbeat state reconstruction , 2007, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[20]  Johann Reger,et al.  An algebraic perspective to single-transponder underwater navigation , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[21]  G. P. Rao,et al.  A general algorithm for parameter identification in lumped continuous systems--The Poisson moment functional approach , 1982 .

[22]  G. Kreisselmeier.  Adaptive observers with exponential rate of convergence , 1977 .