Robust MPC for Asymmetric Input and State Constraints

This paper addresses the issue of dealing with the asymmetric input and state constraints for robust model predictive control (RMPC) in a linear matrix inequality (LMI) framework. In order to handle the asymmetric constraints, a bias term is introduced to input and state respectively such that the symmetric constraints structures are recovered. The invariance of the shifted state is addressed and this condition is utilized for handling the shifted symmetric constraints. It is shown that the proposed approach can reduce the conservativeness of the asymmetric constraint handling in previous results. The recursive feasibility and stability of the proposed approach is guaranteed. A numerical example is shown to illustrate the effectiveness of the proposed approach.