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

M. Lazar, A. Alessio, A. Bemporad, W.P.M.H. Heemels

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)


This paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear systems, possibly affected by disturbances. Given a β-contractive ellipsoidal set script E sign, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets βscript E sign and script E sign. 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 the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.

Original languageEnglish
Title of host publicationProceedings of the 2006 American Control Conference
Number of pages6
Publication statusPublished - 1 Dec 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: 14 Jun 200616 Jun 2006


Conference2006 American Control Conference
Abbreviated titleACC 20116
CountryUnited States
CityMinneapolis, MN


  • Contractive sets
  • Model predictive control
  • Positively invariant sets
  • Robust stability
  • Stability

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