Direct relaxation of hard-constraint in Model Predictive Control

As for MPC controllers, hard-constraint such as constraints on input magnitude or/and rate are generally regarded as an inviolable rule that has to be satisfied strictly before the cost function is optimized at each sampling instant. Such strategy is to result in control conservatism of MPC, as well as infeasibility problem. In this paper, constraint-softening technique is proposed, in which hard-constraint are relaxed appropriately and hence the region of hard-constraint is enlarged directly in optimizer of MPC. As a result, transient performance of the resulting system is significantly improved. Meanwhile, the feasibility problem is solved via this approach. A simulation result demonstrates the effectiveness of the proposed constraint-softening technique.