Prioritized multi‐objective model predictive control without terminal constraints and its applications to nonlinear processes

Many process control problems encapsulate multiple and often conflicting objective criteria spanning different levels of relative importance. In this paper, we consider a class of multi‐objective receding horizon optimal control problems and propose a novel multi‐objective model predictive control (MO‐MPC) scheme for nonlinear systems subject to constraints and several prioritized (economic) criteria. Combining the lexicographic optimization and the receding horizon principle, a prioritized MO‐MPC scheme without terminal constraints is presented to solve economically optimal control problems of the constrained nonlinear system. The results on recursive feasibility and stability of the MO‐MPC are established in the context of economy optimization and no terminal constraints. Particularly, for the systems without state constraints, the computational burden of the MO‐MPC is reduced due to the removal of terminal constraints. Using an intuitive optimizaiton, the feasible set of initial states is offline estimated to move out the initial feasibility condition. The proposed MO‐MPC strategy is verified by the multiple control problems of a coupled‐tank system and a six‐order fluidized bed combustion process.