### Abstract

Original language | English |
---|---|

Pages (from-to) | 2096-2103 |

Number of pages | 8 |

Journal | Automatica |

Volume | 43 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2007 |

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### Cite this

*Automatica*,

*43*(12), 2096-2103. https://doi.org/10.1016/j.automatica.2007.04.028

}

*Automatica*, vol. 43, no. 12, pp. 2096-2103. https://doi.org/10.1016/j.automatica.2007.04.028

**Squaring the circle : an algorithm for generating polyhedral invariant sets from ellipsoidal ones.** / Alessio, A.; Lazar, M.; Bemporad, A.; Heemels, W.P.M.H.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Squaring the circle : an algorithm for generating polyhedral invariant sets from ellipsoidal ones

AU - Alessio, A.

AU - Lazar, M.

AU - Bemporad, A.

AU - Heemels, W.P.M.H.

PY - 2007

Y1 - 2007

N2 - This paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a b-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets bE and E. A proof that the resulting polyhedral set is positively invariant (and contractive under an additional assumption) is given, and a new algorithm is developed to construct the desired polyhedral set. An advantage of the proposed method is that the problem of computing polyhedral invariant sets is formulated as a number of Quadratic Programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is thecomputation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.

AB - This paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a b-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets bE and E. A proof that the resulting polyhedral set is positively invariant (and contractive under an additional assumption) is given, and a new algorithm is developed to construct the desired polyhedral set. An advantage of the proposed method is that the problem of computing polyhedral invariant sets is formulated as a number of Quadratic Programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is thecomputation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.

U2 - 10.1016/j.automatica.2007.04.028

DO - 10.1016/j.automatica.2007.04.028

M3 - Article

VL - 43

SP - 2096

EP - 2103

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 12

ER -