TY  - JOUR
EP  - 1985
ID  - eprints474
N2  - We study model predictive control (MPC) schemes for discrete-time linear time-invariant systems with constraints on inputs and states, that can be formulated using a linear program (LP). In particular, we focus our attention on performance criteria based on a mixed 1 -norm, namely, 1-norm with respect to time and -norm with respect to space. First we provide a method to compute the terminal weight so that closed-loop stability is achieved. We then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it. The piecewise affine
form allows to eliminate online LP, as the computation associated with MPC becomes a simple function evaluation. Besides practical advantages, the availability of the explicit structure of the MPC controller provides an insight into the type of control action in different
regions of the state space, and highlights possible conditions of degeneracies of the LP, such as multiple optima.
SN  - 0018-9286
UR  - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1137550&isnumber=25388
KW  - Constraints; linear programming (LP); model
predictive control (MPC); multiparametric programming; piecewise linear control
TI  - Model Predictive Control Based on Linear Programming - The Explicit Solution
AV  - none
VL  - 47
SP  - 1974
PB  - IEEE 
A1  - Bemporad, Alberto
A1  - Borrelli, Francesco
A1  - Morari, Manfred
IS  - 12
JF  - IEEE Transactions on Automatic Control
Y1  - 2002/12//
ER  -