Abstract:

This letter focuses on a formulation of Model Predictive Control (MPC) with an optimal control problem (OCP) defined by hard input constraints and soft state and terminal set constraints. The soft constraints are accounted for as relaxed barrier function terms in the objective function. The proposed MPC is feasible for any state vector and, assuming the input constraint set is simple (e.g. a hyperrectangle), leads to anytime feasible formulations. A theoretical description of the MPC scheme is conducted. Among other results, asymptotic stability of the proposed MPC is proven and a region of attraction (RoA) estimate is derived. Moreover, stability guarantees when performing a limited number of optimization iterations are also derived. Numerical results showcase the benefit of considering the input constraints directly in the OCP instead of saturating the output of an unconstrained OCP with relaxed barrier functions, as was previously done in the literature.