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

Lazar, Mircea and Alessio, Alessandro and Bemporad, Alberto and Heemels, W.P.M.H. Squaring the circle: An algorithm for generating polyhedral invariant sets from ellipsoidal ones. In: American Control Conference. IEEE, 13th-15th December 2006, pp. 3007-3012. ISBN 1-4244-0209-3 (2006)

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Abstract

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 beta-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets betaE 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 the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs

Item Type: Book Section 10.1109/ACC.2006.1657178 beta-contractive ellipsoidal set; ellipsoidal ones; finite termination; geometrical approach; model predictive control; nonlinear systems; polyhedral invariant set generation; polyhedral positively invariant sets; polyhedral terminal constraint sets; quadratic costs;quadratic programming; robust stability; computational geometry; nonlinear systems; quadratic programming; set theory Q Science > QA MathematicsQ Science > QA Mathematics > QA75 Electronic computers. Computer science Computer Science and Applications Professor Alberto Bemporad 27 Jul 2011 08:43 05 Aug 2011 13:38 http://eprints.imtlucca.it/id/eprint/538