# 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

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topWan, 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 -

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