On stability of multiobjective NMPC with objective prioritization

This paper proposes a new multiobjective model predictive control (MO-MPC) of constrained nonlinear systems. According to objective prioritization, the MO-MPC problem is formulated as a lexicographic optimization problem. The optimal solutions are obtained by solving a hierarchy of single objective optimization problems. The conditions guaranteeing the recursive feasibility of the optimization problem and stability of the closed-loop system are derived, which depend only on the most important objective. Moreover, a suboptimal algorithm is presented to reduce the computational demand of MO-MPC. One characteristic of the proposed MO-MPC is that the given objective prioritization is automatically satisfied. The theoretical results are illustrated by a comparison study of an example.