Partitioning approach oriented to the decentralised predictive control of large-scale systems

In this paper, a partitioning approach for large-scale systems based on graph-theory is presented. The algorithm starts with the translation of the system model into a graph representation. Once the system graph is obtained, the problem of graph partitioning is then solved. The resultant partition consists in a set of non-overlapping subgraphs whose number of vertices is as similar as possible and the number of interconnecting edges between them is minimal. To achieve this goal, the proposed algorithm applies a set of procedures based on identifying the highly connected subgraphs with balanced number of internal and external connections. In order to illustrate the use and application of the proposed partitioning approach, it is used to decompose a dynamical model of the Barcelona drinking water network (DWN). Moreover, a hierarchical-like DMPC strategy is designed and applied over the resultant set of partitions in order to assess the closed-loop performance. Results obtained when used several simulation scenarios show the effectiveness of both the partitioning approach and the DMPC strategy in terms of the reduced computational burden and, at the same time, of the admissible loss of performance in contrast to a centralised MPC strategy.