Overlapping control systems with optimal information exchange

  • Authors:

  • Somayeh Sojoudi;Amir G. Aghdam

  • Affiliations:

  • Department of Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA;Department of Electrical and Computer Engineering, Concordia University, Montréal, QC H3G 1M8, Canada

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

This paper deals with the stabilizability of interconnected systems via linear time-invariant (LTI) decentralized controllers. Given a controllable and observable system with some distinct decentralized fixed modes (DFMs), it is desired to find a suitable control structure (in terms of information flow) for it. Since a decentralized controller consists of a number of non-interacting local controllers, the objective here is to establish certain interactions between the local controllers in order to eliminate the undesirable DFMs. This objective is achieved by translating the knowledge of the system into some bipartite graphs. Then, the notions of minimal sets and maximal subgraphs are introduced, which lead to a simple combinatorial algorithm for solving the underlying problem. The efficacy of the results obtained is demonstrated by an illustrative example.