Control configuration synthesis using agglomerative hierarchical clustering: A graph-theoretic approach

• A graph-theoretic formalism is proposed for control configuration synthesis.
• Relative degree is used as a measure for structural interactions.
• Optimal decentralized control configurations are derived.
• Candidate block decentralized configurations are derived by hierarchical clustering.
• A modularity measure is used to derive the optimal configuration.

This paper addresses the synthesis of control configurations that have optimal structural coupling characteristics between manipulated inputs and controlled outputs in terms of relative degrees. A recently developed agglomerative hierarchical clustering approach is reformulated in a graph theoretic setting. This allows the efficient generation of decentralized control configuration as well as the entire hierarchy of block decentralized control configurations. In addition, a notion of modularity is used to evaluate the compactness and separation of the resulting clusters, allowing the identification of optimal control configurations. The application of the proposed method is illustrated through case studies on an energy integrated fuel-cell system and a heat exchanger network.