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2 results

  • Bang-bang controls of point processes

  • P. Brémaud
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 2 / June 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 385-394
    Print publication:
    June 1976

  • In this paper, we consider the problem of controlling the intensity of a point process in order to maximize the probability that the number of points in a fixed interval equals a given integer, under the constraint that the intensity belong to some closed interval of R+.

    The problem is stated as a problem of optimization on the set of probabilities over the basic measurable space of point processes, and shown to be equivalent to a problem of deterministic control. Structural results concerning the set of optimal solutions are given. The existence of the latter is proven; the control is shown to be bang-bang and a complete solution can be obtained by application of Pontryagin's Maximum Principle.