Document ESAIM: COCV
DOI: 10.1051/cocv:2008025
Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach
Jian Wan, Josep Vehí, Ningsu Luo and Pau HerreroInstitut 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
(Received December 12, 2006. Revised June 11, 2007. Published online March 28, 2008.)
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.
Mathematics Subject Classification. 65G40, 93B05, 93B51
Key words: Nonlinearity, uncertainty, constraints, robust controllable set, quantified set inversion, minimax optimization, interval analysis, modal intervals
© EDP Sciences, SMAI 2008