A multi-step robust model predictive control scheme for polytopic uncertain multi-input systems

摘要

Model predictive control (MPC) has attracted wide attention in process industries with its ability to handle constrained multivariable processes. Computational complexity can become a limiting factor when MPC is applied to large-scale systems with fast sampling times. In this paper, a control scheme known as multi-step robust MPC is presented for polytopic uncertain multi-input systems. Only one or several state feedback laws are optimized at each time interval to reduce computational complexity. A set invariance condition for polytopic uncertain systems is identified and the invariant set is determined by solving a linear matrix inequality (LMI) optimization problem. Based on the set invariance condition, a min-max multi-step robust MPC scheme is proposed. Numerical simulations show the effectiveness of the proposed scheme.