Minimum cost input/output design for large-scale linear structural systems

• Sérgio Pequito ^[1] ; Soummya Kar ^[1] ; A. Pedro Aguiar ^[2]
  1. [1] Carnegie Mellon University

     Carnegie Mellon University

     City of Pittsburgh, Estados Unidos

     
  2. [2] Universidade Do Porto

     Universidade Do Porto

     Santo Ildefonso, Portugal

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 68, 2016, págs. 384-391
• Idioma: inglés
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• Resumen

  • 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.