Geodesic
Stability of integral delay equations and stabilization of age-structured models
Karafyllis, Iasson1   ; Krstic, Miroslav2
1 Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1667-1714

Voir la notice de l'article provenant de la source Numdam

We present bounded dynamic (but observer-free) output feedback laws that achieve global stabilization of equilibrium profiles of the partial differential equation (PDE) model of a simplified, age-structured chemostat model. The chemostat PDE state is positive-valued, which means that our global stabilization is established in the positive orthant of a particular function space–a rather non-standard situation, for which we develop non-standard tools. Our feedback laws do not employ any of the (distributed) parametric knowledge of the model. Moreover, we provide a family of highly unconventional Control Lyapunov Functionals (CLFs) for the age-structured chemostat PDE model. Two kinds of feedback stabilizers are provided: stabilizers with continuously adjusted input and sampled-data stabilizers. The results are based on the transformation of the first-order hyperbolic partial differential equation to an ordinary differential equation (one-dimensional) and an integral delay equation (infinite-dimensional). Novel stability results for integral delay equations are also provided; the results are of independent interest and allow the explicit construction of the CLF for the age-structured chemostat model.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016069
Classification : 34K20, 35L04, 35L60, 93D20, 34K05, 93C23
Keywords: First-order hyperbolic partial differential equation, age-structured models, chemostat, integral delay equations, nonlinear feedback control

Karafyllis, Iasson 1 ; Krstic, Miroslav 2

1 Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA. 
@article{COCV_2017__23_4_1667_0,
     author = {Karafyllis, Iasson and Krstic, Miroslav},
     title = {Stability of integral delay equations and stabilization of age-structured models},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1667--1714},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {4},
     year = {2017},
     doi = {10.1051/cocv/2016069},
     zbl = {1379.35340},
     mrnumber = {3716937},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016069/}
}
TY  - JOUR
AU  - Karafyllis, Iasson
AU  - Krstic, Miroslav
TI  - Stability of integral delay equations and stabilization of age-structured models
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2017
SP  - 1667
EP  - 1714
VL  - 23
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016069/
DO  - 10.1051/cocv/2016069
LA  - en
ID  - COCV_2017__23_4_1667_0
ER  - 
%0 Journal Article
%A Karafyllis, Iasson
%A Krstic, Miroslav
%T Stability of integral delay equations and stabilization of age-structured models
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2017
%P 1667-1714
%V 23
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016069/
%R 10.1051/cocv/2016069
%G en
%F COCV_2017__23_4_1667_0
Karafyllis, Iasson; Krstic, Miroslav. Stability of integral delay equations and stabilization of age-structured models. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1667-1714. doi: 10.1051/cocv/2016069

Cité par Sources :