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Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach

Published online by Cambridge University Press:  23 January 2009

Jian Wan ,
Josep Vehí ,
Ningsu Luo  and
Pau Herrero
Jian Wan
Affiliation:
Institut d'Informàtica i Aplicacions, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain. jwan@eia.udg.edu; vehi@eia.udg.edu; ningsu@eia.udg.edu; pherrero@eia.udg.edu
Josep Vehí
Affiliation:
Institut d'Informàtica i Aplicacions, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain. jwan@eia.udg.edu; vehi@eia.udg.edu; ningsu@eia.udg.edu; pherrero@eia.udg.edu
Ningsu Luo
Affiliation:
Institut d'Informàtica i Aplicacions, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain. jwan@eia.udg.edu; vehi@eia.udg.edu; ningsu@eia.udg.edu; pherrero@eia.udg.edu
Pau Herrero
Affiliation:
Institut d'Informàtica i Aplicacions, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain. jwan@eia.udg.edu; vehi@eia.udg.edu; ningsu@eia.udg.edu; pherrero@eia.udg.edu
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Abstract

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

Nonlinearityuncertaintyconstraintsrobust controllable setquantified set inversionminimax optimizationinterval analysismodal intervals
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 1 , January 2009 , pp. 189 - 204
Copyright
© EDP Sciences, SMAI, 2008

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