%0 Book Section
%A Bemporad, Alberto
%A Borrelli, Francesco
%A Morari, Manfred
%B European Control Conference
%C Porto, Portugal
%D 2001
%F eprints:578
%I European Control Conference
%P 939-944
%T Piecewise linear robust model predictive control
%U http://eprints.imtlucca.it/578/
%X For discrete-time linear time-invariant systems with input disturbances and constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to robust optimal control problems based on min-max optimization. We show that the optimal control sequence is a piecewise linear function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the on-line computation of the resulting MPC controller is reduced to a simple linear function evaluation. In this paper the uncertainty is modeled as an additive norm-bounded input disturbance vector. The technique can be also extended to robust control of constrained systems affected by polyhedral parametric uncertainty.