TY  - JOUR
EP  - 1480 
ID  - eprints1051
N2  - This paper investigates stochastic stabilization procedures based on quadratic and piecewise linear Lyapunov functions for discrete-time linear systems affected by multiplicative disturbances and subject to linear constraints on inputs and states. A stochastic model predictive control (SMPC) design approach is proposed to optimize closed-loop performance while enforcing constraints. Conditions for stochastic convergence and robust constraints fulfillment of the closed-loop system are enforced by solving linear matrix inequality problems off line. Performance is optimized on line using multi-stage stochastic optimization based on enumeration of scenarios, that amounts to solving a quadratic program subject to either quadratic or linear constraints. In the latter case, an explicit form is computable to ease the implementation of the proposed SMPC law. The approach can deal with a very general class of stochastic disturbance processes with discrete probability distribution. The effectiveness of the proposed SMPC formulation is shown on a numerical example and compared to traditional MPC schemes.
SN  - 0018-9286
UR  - http://eprints.imtlucca.it/1051/
KW  - Model predictive control 
KW  -  constrained linear systems 
KW  -  stochastic control 
AV  - none
TI  - Stabilizing model predictive control of stochastic constrained linear systems
VL  - 57
SP  - 1468 
PB  - IEEE 
A1  - Bernardini, Daniele
A1  - Bemporad, Alberto
IS  - 6
JF  - IEEE Transactions on Automatic Control 
Y1  - 2012/07//
ER  -