On an Optimization Problem in Sensor Selection

  • Authors:

  • Rami Debouk;Stéphane Lafortune;Demosthenis Teneketzis

  • Affiliations:

  • Department of Electrical Engineering and Computer Science, The University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109-2122, U.S.A. rami.debouk@gm.com;Department of Electrical Engineering and Computer Science, The University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109-2122, U.S.A. stephane@eecs.umich.edu;Department of Electrical Engineering and Computer Science, The University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109-2122, U.S.A. teneketzis@eecs.umich.edu

  • Venue:
  • Discrete Event Dynamic Systems
  • Year:
  • 2002

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Abstract

We address the following sensor selection problem. We assume that a dynamic system possesses a certain property, call it Property D, when a set Γ of sensors is used. There is a cost cA associated with each set A of sensors that is a subset of Γ. Given any set of sensors that is a subset of Γ, it is possible to determine, via a test, whether the resulting system-sensor combination possesses Property D. Each test required to check whether or not Property D holds incurs a fixed cost. For each set of sensors A that is a subset of Γ there is an a priori probability pA that the test will be positive, i.e., the system-sensor combination possesses Property D. The objective is to determine a test strategy, i.e., a sequence of tests, to minimize the expected cost, associated with the tests, that is incurred until a least expensive combination of sensors that results in a system-sensor combination possessing Property D is identified. We determine conditions on the sensor costs cA and the a priori probabilities pA under which the strategy that tests combinations of sensors in increasing order of cost is optimal with respect to the aforementioned objective.