Entropy-based empirical relations between original and reduced state variables

In projection-based model reduction methods, the reduced basis which approximates the original dynamics is derived from the main dynamical features inferred from the collected state variable evolutions, controllability, or observability Gramians. However, the relations between original and reduced state variables are not explicitly available since all original state variables are entangled in the reduced basis. This paper presents an empirical method developed from the Shannon entropy concept which identifies the individual relations between the original and reduced state variables. The empirical relations are applied in the closed loop control design of a spatio-temporal model reduced by the POD method. The incorporation of the empirical relations in the closed loop design results in a more effective closed loop performance