Dantzig-wolfe Decomposition and Large-scale Constrained Mpc Problems

Model Predictive Control (MPC) strategies are typically implemented in two levels: a steady-state target calculation and a control calculation. The steady-state target calculation consumes excess degrees of freedom within the control problem to provide optimal steady-state performance with respect to some specified objective. In some MPC approaches, the target calculation is formulated as a Linear Program (LP) with a pre-specified objective function and a linear or linearized steady-state model derived from that used in the control calculation. In large-scale problems, centralized MPC schemes find the optimal solution for the plant-wide optimization problem, but may not provide sufficient redundancy or reliability and can require substantial computation. On the other hand, in a decentralized MPC scheme, the target calculations are performed independently by ignoring interactions among units, and as a result will not usually find the optimal operation. In contrast to the centralized MPC approach, a decentralized MPC provides a high degree of redundancy with respect to the failure of an individual MPC. For largescale process control problems, the desired characteristics for an MPC implementation include: accurate and quick tracking of the changing optimal steady-state operation, a high degree of reliability with respect to failure within the MPC application (i.e., failure of a portion of the control system), and low computational requirements. Fully centralized or monolithic MPC and independent block-wise decentralized MPC represent the two extremes in the “trade-off” among the desired characteristics of an implemented MPC system. In this paper, we propose a coordinated, decentralized approach to the steady-state target calculation problem. Our approach is based on the Dantzig-Wolfe decomposition principle and has been found to be effective at finding the optimal plant operation while providing a high degree of reliability at a reasonable computational load.