An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems

An off-line Model Predictive Control (MPC) method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances. In order to reduce the computational burdens and conservativeness of traditional polytopic MPC schemes, the present approach carries out off-line most of the computations and it makes use of closed-loop predictions to improve the control performance. This is done by recursively pre-computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on-line a simple and numerically low-demanding optimization problem subject to a set-membership constraint. Comparisons with three other recent off-line MPC approaches are also provided in the final example.