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.

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.

DOI : 10.1051/cocv:2008025
Classification : 65G40, 93B05, 93B51
Mots-clés : nonlinearity, uncertainty, constraints, robust controllable set, quantified set inversion, minimax optimization, interval analysis, modal intervals 
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     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},
     publisher = {EDP-Sciences},
     volume = {15},
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     url = {http://www.numdam.org/articles/10.1051/cocv:2008025/}
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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. http://www.numdam.org/articles/10.1051/cocv:2008025/

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