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Minimum Cost Structural Input/Output Selection for Large-Scale Linear Time-Invariant Systems



title = "Minimum cost input/output design for large-scale linear structural systems ",
journal = "Automatica ",
volume = "68",
number = "",
pages = "384 - 391",
year = "2016",
note = "",
issn = "0005-1098",
doi = "",
url = "",
author = "Sérgio Pequito and Soummya Kar and A. Pedro Aguiar",
keywords = "Linear structural systems",
keywords = "Input/output selection",
keywords = "Graph theory",
keywords = "Computational complexity ",
abstract = "Abstract In this paper, we provide optimal solutions to two different (but related) input/output design problems involving large-scale linear dynamical systems, where the cost associated to each directly actuated/measured state variable can take different values, but is independent of the input/output performing the task. Under these conditions, we first aim to determine and characterize the input/output placement that incurs in the minimum cost while ensuring that the resulting placement achieves structural controllability/observability. Further, we address a constrained variant of the above problem, in which we seek to determine the minimum cost placement configuration, among all possible input/output placement configurations that ensures structural controllability/observability, with the lowest number of directly actuated/measured state variables. We develop new graph-theoretical characterizations of cost-constrained input selections for structural controllability and properties that enable us to address both problems by reduction to a weighted maximum matching problem — efficiently addressed by algorithms with polynomial time complexity (in the number of state variables). Finally, we illustrate the obtained results with an example. "