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Submodularity of Energy Related Controllability Metrics


F. Cortesi, T.H. Summers, J. Lygeros

IEEE Conference on Decision and Control, Los Angeles

The quantification of controllability and observ- ability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of actuators and sensors that optimize real-valued controllability and observability metrics of the network. We show that several classes of energy related metrics associated with the controllability Gramian in linear dynamical systems have a strong structural property, called submodularity. This property allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and for placement of power electronic actuators in a model of the European power grid.


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% Autogenerated BibTeX entry
@InProceedings { CorSum:2014:IFA_4713,
    author={F. Cortesi and T.H. Summers and J. Lygeros},
    title={{Submodularity of Energy Related Controllability Metrics}},
    booktitle={IEEE Conference on Decision and Control},
    address={Los Angeles},
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