Article

Discrete Event Dynamic Systems

, Volume 12, Issue 4, pp 417-445

On an Optimization Problem in Sensor Selection*

  • Rami DeboukAffiliated withDepartment of Electrical Engineering and Computer Science, The University of Michigan
  • , Stéphane LafortuneAffiliated withDepartment of Electrical Engineering and Computer Science, The University of Michigan
  • , Demosthenis TeneketzisAffiliated withDepartment of Electrical Engineering and Computer Science, The University of Michigan

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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.

failure diagnosis hypothesis testing Markovian decision problems optimization sensor selection