Use of Mixed-integer Formulations in Predictive Control Algorithms

Most industrial model predictive controllers (MPC) use the traditional two-layer structure developed in the early 1980’s, where the upper layer defines optimal steady-state targets for inputs and outputs, while the lower layer calculates the control moves that drive the system towards these steady-state targets. As a rule, both layers use continuous quadratic programming (QP) formulations to derive the optimal solutions. On the other hand, the advances in mixed-integer programming (MIP) algorithms and their successful utilization to solve large scheduling problems in reasonable time show that MIP formulations have the potential of being advantageously applied to the multivariable model predictive control problem. In this paper we present a mixed-integer quadratic programming (MIQP) formulation for the steady state targets calculation layer, and show that several difficulties faced in the MPC practical implementation can be overcome with this approach. 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 was applied to a simulated industrial system and the results compared with those achieved by a traditional continuous MPC.