Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 863-869 |
| Number of pages | 7 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 47 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2002 |
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On hybrid systems and closed-loop MPC systems. / Bemporad, A.; Heemels, W.P.M.H.; Schutter, de, B.
In: IEEE Transactions on Automatic Control, Vol. 47, No. 5, 2002, p. 863-869.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - On hybrid systems and closed-loop MPC systems
AU - Bemporad, A.
AU - Heemels, W.P.M.H.
AU - Schutter, de, B.
PY - 2002
Y1 - 2002
N2 - The following five classes of hybrid systems were recently proven to be equivalent: linear complementarity, extended linear complementarity, mixed logical dynamical systems, piecewise affine systems and max-min-plus-scaling systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of certain system variables. In this paper, for linear or hybrid plants in closed-loop with a model predictive control (MPC) controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion, we provide a simple and direct proof that the closed-loop system is a subclass of any of the former five classes of hybrid systems. This result is of extreme importance, as it opens up the use of tools developed for the mentioned hybrid model classes, such as (robust) stability and safety analysis tools, to study closed-loop properties of MPC.
AB - The following five classes of hybrid systems were recently proven to be equivalent: linear complementarity, extended linear complementarity, mixed logical dynamical systems, piecewise affine systems and max-min-plus-scaling systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of certain system variables. In this paper, for linear or hybrid plants in closed-loop with a model predictive control (MPC) controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion, we provide a simple and direct proof that the closed-loop system is a subclass of any of the former five classes of hybrid systems. This result is of extreme importance, as it opens up the use of tools developed for the mentioned hybrid model classes, such as (robust) stability and safety analysis tools, to study closed-loop properties of MPC.
U2 - 10.1109/TAC.2002.1000287
DO - 10.1109/TAC.2002.1000287
M3 - Article
VL - 47
SP - 863
EP - 869
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 5
ER -