A general framework for computing robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed robust controllable sets is introduced in this paper. The addressed one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solver of 1-dimensional quantified set inversion in modal interval analysis is extended to 2-dimensional cases for computing robust controllable sets off-line with a clear semantic interpretation, where both universal and existential quantifiers are concerned simultaneously. An interval-based solver of constrained minimax optimization is also proposed to compute one-step control inputs online in a reliable way, which guarantee to drive the system state contractively along the computed robust controllable sets to a selected terminal robust control invariant set.
Keywords: nonlinearity, uncertainty, constraints, robust controllable set, quantified set inversion, minimax optimization, interval analysis, modal intervals
@article{COCV_2009__15_1_189_0,
author = {Wan, Jian and Veh{\'\i}, Josep and Luo, Ningsu and Herrero, Pau},
title = {Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets : a modal interval analysis approach},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {189--204},
year = {2009},
publisher = {EDP-Sciences},
volume = {15},
number = {1},
doi = {10.1051/cocv:2008025},
mrnumber = {2488575},
zbl = {1158.93010},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008025/}
}
TY - JOUR AU - Wan, Jian AU - Vehí, Josep AU - Luo, Ningsu AU - Herrero, Pau TI - Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets : a modal interval analysis approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 189 EP - 204 VL - 15 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008025/ DO - 10.1051/cocv:2008025 LA - en ID - COCV_2009__15_1_189_0 ER -
%0 Journal Article %A Wan, Jian %A Vehí, Josep %A Luo, Ningsu %A Herrero, Pau %T Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets : a modal interval analysis approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 189-204 %V 15 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008025/ %R 10.1051/cocv:2008025 %G en %F COCV_2009__15_1_189_0
Wan, Jian; Vehí, Josep; Luo, Ningsu; Herrero, Pau. Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets : a modal interval analysis approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 189-204. doi: 10.1051/cocv:2008025
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