Model Predictive Control for Linear Systems under Relaxed Constraints

This article considers model predictive control (MPC) for linear systems under relaxed constraints. The main novelty of our proposal is the introduction, and an adequate use, of the terminal dynamics of the slack variable associated with relaxed constraints. The proposed MPC under relaxed constraints retains computational efficiency of the traditional MPC, while it guarantees positive invariance and exponential stability over an enlarged domain of attraction. The design method is also illustrated in a step-by-step manner by an academic example.