Hierarchical clustering of constrained dynamic systems using robust positively invariant sets

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A systematic Agglomerative Hierarchical Clustering (AHC) approach based on minimal Robust Positively Invariant (mRPI) sets is presented for decomposing linear constrained dynamic systems. Specifically, a novel distance metric is proposed where the distance between neighboring subsystems is computed based on the volume of the mRPI sets. Through this distance metric, the proposed AHC approach simultaneously accounts for subsystem dynamics, the constraints on states and inputs, and disturbances created by the dynamic coupling between subsystems. A combination of simple and complex numerical examples is used to demonstrate the key features of the approach including the sensitivity of the proposed AHC to system structure, parameters, and constraints. Finally, numerical results show the benefit of using the proposed AHC when determining potential system decompositions for robust decentralized Model Predictive Control (MPC).