We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K, Q). If the stable subgroup of the uncontrolled system is closed and K has positive measure for a left invariant Haar measure, the upper bound coincides with the outer invariance entropy.
Accepté le :
Première publication :
Publié le :
Keywords: Invariance entropy, linear systems, discrete-time control systems, Lie groups
@article{COCV_2021__27_1_A57_0,
author = {Colonius, Fritz and Cossich, Jo\~ao A. N. and Santana, Alexandre J.},
title = {Outer invariance entropy for discrete-time linear systems on {Lie} groups},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021054},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021054/}
}
TY - JOUR AU - Colonius, Fritz AU - Cossich, João A. N. AU - Santana, Alexandre J. TI - Outer invariance entropy for discrete-time linear systems on Lie groups JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021054/ DO - 10.1051/cocv/2021054 LA - en ID - COCV_2021__27_1_A57_0 ER -
%0 Journal Article %A Colonius, Fritz %A Cossich, João A. N. %A Santana, Alexandre J. %T Outer invariance entropy for discrete-time linear systems on Lie groups %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021054/ %R 10.1051/cocv/2021054 %G en %F COCV_2021__27_1_A57_0
Colonius, Fritz; Cossich, João A. N.; Santana, Alexandre J. Outer invariance entropy for discrete-time linear systems on Lie groups. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 55. doi: 10.1051/cocv/2021054
[1] and , To appear Dynamics of endomorphisms of Lie groups and their topological entropy..
[2] , , and , Control sets of linear systems on semi-simple Lie groups. J. Diff. Equ. 269 (2020) 449–466.
[3] , and , Control sets of linear systems on Lie groups. Nonlinear Differ. Equ. Appl. 24 (2017) 7–15.
[4] , Entropy for group endomorphisms and homogeneous spaces. Trans. Am. Math. Soc. 153 (1971) 401–414.
[5] , and , Controllability properties and invariance pressure for linear discrete-time systems, J. Dyn. Differ. Equ. (2021), DOI . | DOI
[6] and , Invariance entropy for control systems. SIAM J. Control Optim. 48 (2009) 1701–1721.
[7] , Outer invariance entropy for linear systems on Lie groups. SIAM J. Control Optim. 52 (2014) 3917–3934.
[8] , Controllability of linear systems on solvable Lie groups. SIAM J. Control Optim. 54 (2016) 372–390.
[9] and , Invariance entropy of hyperbolic control sets. Discr. Continu. Dyn. Syst. 36 (2016) 97–136.
[10] and , Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds. Israel J. Math. 232 (2019) 947–1000.
[11] , Invariance entropy of control sets. SIAM J. Control Optim. 49 (2011) 732–751.
[12] , Invariance Entropy for Deterministic Control Systems. An Introduction. Vol. 2089 of LNM. Springer, Berlin (2013).
[13] , Lie Groups Beyond an Introduction, Second Edition, Birkhäuser (2002).
[14] , , and , Topological feedback entropy and nonlinear stabilization. IEEE Trans. Aut. Control 49 (2004) 1585–1597.
[15] , Grupos de Lie, Editora Unicamp, 2016 Campinas.
[16] , Mathematical Control Theory. Deterministic Finite Dimensional Systems, 2nd edn. Springer-Verlag, New York (1998).
[17] , An Introduction to Ergodic Theory. Springer-Verlag (1982).
Cité par Sources :
