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

Jian Wan; Josep Vehí; Ningsu Luo; Pau Herrero

ESAIM: Control, Optimisation and Calculus of Variations (2009)

  • Volume: 15, Issue: 1, page 189-204
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Wan, Jian, et al. "Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach." ESAIM: Control, Optimisation and Calculus of Variations 15.1 (2009): 189-204. <http://eudml.org/doc/250563>.

@article{Wan2009,
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. },
author = {Wan, Jian, Vehí, Josep, Luo, Ningsu, Herrero, Pau},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Nonlinearity; uncertainty; constraints; robust controllable set; quantified set inversion; minimax optimization; interval analysis; modal intervals; nonlinearity; robust controllable set; interval analysis},
language = {eng},
month = {1},
number = {1},
pages = {189-204},
publisher = {EDP Sciences},
title = {Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach},
url = {http://eudml.org/doc/250563},
volume = {15},
year = {2009},
}

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
DA - 2009/1//
PB - EDP Sciences
VL - 15
IS - 1
SP - 189
EP - 204
AB - 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.
LA - eng
KW - Nonlinearity; uncertainty; constraints; robust controllable set; quantified set inversion; minimax optimization; interval analysis; modal intervals; nonlinearity; robust controllable set; interval analysis
UR - http://eudml.org/doc/250563
ER -

References

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