A mixed-integer model predictive control formulation for linear systems

• Development of mixed-integer quadratic formulation for model predictive controllers.
• The formulation allows the assignment of explicit priorities for the outputs and for the inputs.
• The formulation was successfully tested in simulated benchmarks and in an industrial case.
• The computational effort is not greatly increased when compared to the continuous MPC.

Since their inception in the early 1980s industrial model predictive controllers (MPC) rely on continuous quadratic programming (QP) formulations to derive their optimal solutions. More recent advances in mixed-integer programming (MIP) algorithms show that MIP formulations have the potential of being advantageously applied to the MPC problem. In this paper, we present an MIP formulation that can overcome difficulties faced in the practical implementation of MPCs. In particular, it is possible to set explicit priorities for inputs and outputs, define minimum moves to overcome hysteresis, and deal with digital or integer inputs. The proposed formulation is applied to simulated process systems and the results compared with those achieved by a traditional continuous MPC. The solutions of the resulting mixed-integer quadratic programming (MIQP) problems are derived by a computer implementation of the Outer Approximation method (OA) also developed as part of this work.