Model Predictive Control of Interacting Systems - Effect of Control Architecture*

Model predictive control (MPC) is one of the most commonly used advanced controllers for industrial applications. Implementation of MPC requires solving computationally expensive constrained optimization problem in a limited time interval. Decentralized and distributed MPC formulations aim at decomposing a large control problem into multiple small problems, which can be solved at a faster rate. The closed-loop performance of these formulations strongly depends on the decomposition (segregation of inputs and outputs into sub-controllers), which is typically done based on intuition. Obtaining an optimal decomposition for highly interacting systems is not trivial. In this paper, we apply graph theory-based approach to decompose a large control problem with an objective of improving the closed-loop performance of the resulting distributed and decentralized formulations. The control problem is first abstracted as a weighted digraph to transform the controller decomposition problem into a graph partition problem. Using the well-known concept of community structure, control architectures are synthesized for decentralized and distributed MPC. The proposed methodology is illustrated using an octuple tank system. Using a simulation case study, the closed-loop performance of various control architectures is compared and it is demonstrated that the control architectures derived using graph theory perform better than intuition-based architectures.