TY  - JOUR
SP  - 2096
PB  - Elsevier
A1  - Alessio, Alessandro
A1  - Lazar, Mircea
A1  - Bemporad, Alberto
A1  - Heemels, W.P.M.H.
IS  - 12
JF  - Automatica
Y1  - 2007///
VL  - 43
N2  - This paper presents a new (geometrical) approach to the computation of polyhedral (robustly) positively invariant (PI) sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a ?-contractive ellipsoidal set View the MathML source, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets View the MathML source and View the MathML source. A proof that the resulting polyhedral set is contractive and thus, PI, is given, and a new algorithm is developed to construct the desired  polyhedral set. 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.

SN  - 0005-1098
UR  - http://www.sciencedirect.com/science/article/pii/S0005109807003032
KW  - Positively invariant sets; Contractive sets; Model predictive control; Stability; Robust stability
AV  - none
TI  - Squaring the circle: an algorithm for generating polyhedral invariant sets from ellipsoidal ones
EP  - 2103
ID  - eprints479
ER  -