A novel graph-based partitioning algorithm for large-scale dynamical systems

In this paper, a novel graph-based system partitioning approach is proposed to facilitate the design of distributed or decentralised control in large-scale dynamical systems. In large-scale dynamical systems, a decomposition method is required to determine a suitable set of distributed subsystems and their relevant variables. In the proposed approach, a decomposition algorithm starts to generate an overall graph representation of the system model in the form of a new weighted digraph on the basis of a sensitivity analysis concept to quantify the coupling strengths among the system variables in terms of graph edge weights. The produced weighted digraph and its structural information are then used to partition the system model. All the potential system control inputs are first characterised as the main graph vertices, representing fixed subsystems centres. Then, the remaining vertices, representing system states or outputs, are assigned to the created subgraphs. Once the initial grouping is accordingly formed, a merging routine is automatically conducted to merge the small subgraphs in other subgraphs in an iterative searching way to find the smaller cut sizes. Each time a merging occurs, the total cost of the merged configuration, being defined in terms of an averaged linear quadratic regulator (LQR) metric, is used as a novel dynamic performance metric versus total group number reduction to terminate the algorithm for the best grouping result. A chemical industrial process plant is used as a benchmark to assess performance of the proposed methodology to fulfil the system partitioning objective. The output result of the algorithm is then comparatively used for a decentralised non-linear model-based predictive control methodology to demonstrate its ultimate merits.